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THE 


ELEMEJNTS   OF  LOGIC 


CAPACITY  OF  YOUNGER  STUDENTS. 


DESIGNED  FOR  ACADEMIES  AND  THE  HIGHEK 
CLASSES  OF  COMMON  SCHOOLS. 


By  CHARLES   K.  TRUE,  D.D. 


Nihil  difficile  amantL—OiOBRa 


NEW  YORK :  HUNT  &  EATON 
CINCINNATI :  CRANSTON  &  CURTS 


UNIVERSITY    i 


Entered  according  to  Act  of  Congress,  in  the  year  1860. 

Bt  CARLTON  &  PORTER, 

in  the  Clerk's  Office  of  the  District  Court  of  the  United  States  foi 
the  Southern  District  of  New- York. 


'^^  Of    THE 

UNIVERSITY 

Of 


PREFACE. 


Logic,  as  a  science,  is  simple  and 
limited.  Most  modern  treatises  upon  the 
subject  have  erred,  by  extending  it  be- 
yond its  proper  department,  on  the  one 
hand,  and  by  excluding  it  from  its  legiti- 
mate province  on  the  other.  By  some  it 
has  been  made  to  occupy  the  ground  of 
mental  science  or  of  rhetoric ;  by  others  it 
has  been  denominated,  "  amj  art  of  reason- 
ing," as  if  there  were  any  sound  reasoning 
which  is  not  logical,  while  others  have 
claimed  for  it  the  unlimited  sphere  of 
teaching  "  the  right  use  of  reason."  These 
errors  have  been  exposed  by  Archbishop 


1:  PREFACE. 

Whately,  and  the  true  nature  and  ap- 
propriate office  of  logic  have  been  ex- 
plained and  vindicated.  His  learned  and 
able  treatise  has  obtained  favor  in  the 
universities  of  Great  Britain  and  the 
United  StatCi^,  and  will  go  far,  undoubt- 
edly, to  revive  and  extend  a  neglected, 
but  invaluable  science.  The  principles  of 
that  work,  which  are  none  other  than 
those  of  Aristotle,  have  been  adopted  as 
the  basis  of  the  present  volume. 

The  treatise  now  presented  to  the 
public  is  designed  for  a  department 
hitherto  unoccupied. 

A  science,  so  rudimentary  in  its  prin- 
ciples, and  so  extensive  in  its  applications, 
ought  to  be  studied  with  the  common 
elements  of  learning.  Nor,  when  prop- 
erly explained,  will  it  be  found  any  more 
difficult  to  the  younger  student  than 
grammar  or  arithmetic.     It  will  not  task 


PREFACE. 


the  powers  beyond  what  is  desirable  in 
salutary  discipline,  while  its  tendency  to 
promote  a  habit  of  •  thinking  will  be 
greater  than  that  of  any  other  science. 
Indeed,  logic  must  be  studied  early,  and 
rendered  perfectly  familiar,  in  order  to  be 
of  much  practical  utility  in  the  business 
of  life.  It  is  so  long  postponed  in  existing 
systems  of  education,  and,  after  all,  so 
superficially  studied,  that  there  is  scarcely 
one  educated  man  in  a  thousand  who  pro- 
fesses to  be  master  of  logic. 

This  work,  though  simple  in  its  arrange- 
ment, embraces  all  that  is  essential  to 
logic,  while  everything  which  does  not 
strictly  and  necessarily  come  within  the 
appropriate  province  of  the  science  has 
been  excluded.  Collateral  matter  and 
discumve  explanations  have  been  avoided, 
as  rather  calculated  to  embarrass  and  con- 
fuse the   youthful   mind.     The  principles 


6  PREFACE. 

and  rules  of  the  science  have  l»een  stated 
distinctly,  and  illustrated  by  a  variety  of 
examples.  If  any  •further  explanation  is 
necessary  the  enlightened  teacher  can 
easily  supply  it.  The  great  points  will 
thus  stand  out  prominently  to  view,  and 
all  that  is  added  by  way  of  comment  will 
be  associated  with  them  in  the .  mind. 
The  attention  of  the  learner  wiU  not  be 
distracted  by  many  particulars,  nor  the 
memory  encumbered  with  unessential 
matter. 
Boston,  August  14,  1840. 


Of    THE 

UNIVERSITY 

Of 


PREFACE  TO  THE  REVISED  EDITION. 


The  first  edition  of  this  book  has  been 
used  chiefly  in  academies  of  a  high  grade 
and  as  a  manual  in  some  colleges.  The 
improvements  in  this  edition  will  make  it 
still  more  acceptable  to  advanced  students, 
while  it  will  be  no  less  adapted  to  the 
object  for  which  it  was  originally  de- 
signed, namely,  to  follow  immediately 
after  grammar  in  all  schools  where  the 
higher  branches  are  commenced.  Will 
teachers  of  grammar  schools  now  give 
this  book  a  trial,  and  make  known  to 
the  public  the  results  of  the  experiment  ? 
Consider :  Will  it  not  be  of  the  greatest 


b  t»REFACE  TO  THE   REVISED   EDITION. 

advantage  to  form  the  habit  in  early 
life  of  analyzing  one's  process  of  thought 
in  reasoning,  and  especially  observing 
whether  the  reason  given  for  an  opinion 
is  a  general  reason.  For  example:  It  is 
of  itself  no  proof,  that  you  are  not  at 
the  scene  of  a  murder,  because  you  are 
here.  Indeed!  what  other  proof  is  neces- 
sary? Clearly  this  general  prmdple — 
that  no  being  but  God  can  be  in  two 
places  at  the  same  time.  Without  this 
as  a  major  premise,  your  alibi  as  a  minor 
premise  answers  no  purpose.  To  be  sure 
this  principle  is  implied  in  the  minor 
premise,  and  it  happens  to  be  a  sound 
one ;  but  how  often  in  practical  life  do 
we  imply  in  our  statements  a  general 
Drinciple  which  is  not  sound;  but  its 
unsoundness  escapes  us,  because  we  are 
not  in  the  habit  of  considering  it  dis- 
tinctively.     It    would    be    easy    enough 


PBEFAOE  TO  THE  EE VISED   EDITION.         9 

to  give  illustration  of  this  from  any 
political  or  religious  newspaper  that 
comes  to  hand.  I  insist,  therefore,  that 
a  science  so  pertinent  to  every-day 
practical  life  should  not  be  excluded 
from  elementary  studies,  but  should  be 
taught  in  every  grammar  school. 

The  most  important  improvements  in 
this  edition  are  the  Analytical  Outline, 
the  Chapter  on  Distinctions  of  Reason- 
ing, and  the  Essay  on  the  Philosophy  of 
Induction. 

New  Yokk,  October,  1860. 


CONTENTS. 


tMm 

Analytical  Outlinb 13 

PART  I.— ON  TERMS. 

SacTioii 

I.  Different  Kinds  of  Terms 23 

II.  Opposition  of  Terms 26 

HI.  Species  and  Genus 28 

IV.  Division *. 30 

V.  Definition 31 


PART  II.— PROPOSITIONS. 

I.  Parts  of  a  Proposition 36 

11.  Distinction  of  Propositions 37 

III.  Further  Distinctions 41 

IV.  Distribution  of  Terms  of  Propositions 43 

V.  Opposition 46 

VL  Conversion 52 

PART  in.— ARGUMENTS. 

Definition  of  Arguments 511 

1.  Syllogisms 58 

n.  Rules  of  Syllogism *  61 

in.  Irregular  Syllogisms 71 

rv.  Hypothetical  Syllogism. — Dilemma 77 

V.  Distinctions  of  Reasoning 83 


12  CONTENTS. 

PART  IT.— FALLACIES. 

PAas 

DisnNCTiON  OP  Fallacies 95 

L  Logical  Fallacies 98 

U.   MATERLA.L  FALLACIES 102 

SUPPLEMENT. 

L  Moods  and  Figures  op  Syllogisms. 107 

II.  Reduction 114 

Questions  in  Review 120 

APPENDIX. 

I.  Dissertation  on  Induction 121 

FL  Miscellaneous  Examples  for  Practice 152 

Supposed  Exceptions  to  Rules 168 


ELEMENTS  OF  LOGIC, 


INTKODUCTION. 

ANALYTICAL     OUTLINE. 

1.  IjOGio  is  the  science  of  inference;  it  teaches 
how  one  judgment  may  be  inferred  from  other 
judgments.  To  reason  is  to  infer,  hence  it  is 
usually  called  tEe  science  of  reasoning. 

2.  It  assumes  that  every  mind  conceives  in- 
tuitively some  ideas  or  judgments  which  are 
at  once  primary  and  certain ;  otherwise  we  could 
have  no  foundation  for  inference ;  and  to  infer 
one  idea  or  judgment  from  others  would  give  # 
no  certainty. 

These  ideas  are  called  first  truths.  They  are 
given  by  the  senses,  the  consciousness,  and  the 
reason,  and  are  innumerable.  I  exist  There 
is  an  external  world.     This  hodnj  is  sclid^  ex- 


14  ELEMENTS  OF  LOGIC. 

tended^  rounds  red,  warm,  or  cold,  are  first 
truths. 

3.  At  first  these  ideas  are  particular,  but 
afterward  the  mind  unites  those  which  are  the 
same  in  some  respect  into  classes  by  simple  ad- 
dition. This  is  called  genq^j^lization.  To  ex 
press  this  we  no  longer  say,  This  hody^  a/nd 
that  hody,  and  yonder  hody^  etc.,  but  hod/y. 
Red  hody  would  be  a  lower  class  made  up  of 
this  red  thing,  that  red  thing,  etc. 

4.  It  is  evident,  furthermore,  that  in  order  to 
reason  the  mind  must  have  some  general  ideas, 
or  judgments,  that  are  conceived  intuitively, 
and  not  formed  by  mere  addition  or  generali-' 
zation ;  for  if  you  make  a  class  by  adding  all 
the  individuals,  you  gain  nothing  by  drawing 
one  or  more  out  again.  These  general  ideas  are 
called  first  principles,  or  axioms,  and  are  the 
offspring  of  the  reason.  Some  of  the  earliest 
are  these :  Every  hody  is  in  space.  No  event 
happens  without  a  cause.  lAJce  material  causes 
produce  like  effects. 

5.  It  is  the  province  of  psychology  to  explain 
under  what  circumstances  these  primary  ideas 
are  given  by  the  senses,  the  consciousness,  and 
the  reason;  but  logic  assumes  their  existence 


ANALYTICAL  OUTLINE.  16 

as  the  indispensable  basis  of  inference,  and  its 
appropriate  office  is  to  explain  in  what  way 
we  infer  one  judgment  from  another. 

6.  The  process  of  reasoning  when  completed 
is  found  to  be  simply  this :  Something  is  jpredi- 
ca^ed^  that  is^  affirmed  or  denied  of  a  class  /  an 
individual  is  affirmed  to  belong  to  this  class, 
and  then,  of  course,  the  same  thing  can  he  af 
f/rmed  or  denied  of  thai  vndividual. 

In  whatever  form  a  sound  argument  is  ex- 
pressed, it  may  always  be  shown  to  involve  this 
process,  and  every  unsound  argument  deviates 
from  it.  In  reasoning  we  always  proceed  from 
generals  to  particulars,  and  never  from  particu- 
lars to  generals,  for  this  is  impossible,  as  it  would 
be  to  draw  out  what  was  never  put  in.  A  gene- 
ral principle,  to  be  sure,  may  be  inferred  from  one 
still  more  general ;  but  in  relation  to  that  more 
general  principle  it  is  only  a  particular ;  it  is  a 
class  in  a  class  of  classes — a  species  under  a 
genus.  For  example,  the  general  law  of  ter- 
restrial gravity  is  an  inference,  not  from  par- 
ticular instances  of  bodies  falling  to  the  earth, 
but  from  a  more  general  law,  which  these  par- 
ticulars indicate.  This  is  an  instance  of  in- 
duction. 


16  ELEMENTS  OF  LOGIC. 

7.  As  induction  has  been  supposed  to  be  a 
mode  of  reasoning  opposite  to  deduction,  let 
us  take  a  simple  and  common  case.  I  infer  that 
heat  to  such  a  degree  as  will  cause  the  mercury 
in  the  thermometer  to  rise  to  the  point  marked 
two  hundred  and  twelve  degrees  on  Fahrenheit's 
thermometer  will  always  ca/me  water  to  hoil  ^ 
in  other  words,  it  is  proved  by  induction  to 
be  a  law  of  nature  that  two  himdred  and 
twel/oe  degrees  Fahrenheit  will  cause  water  to 
hail. 

Now  this  conclusion  is  not  drawn  from  any 
number  of  instances  of  the  boiling  of  water,  but 
from  a  few  instances  combined  with  the  prin- 
ciple that  like  cause  will  produce  like  effects; 
for  if  this  principle  were  not  true,  then  forty 
thousand  instances  of  water  boiling  by  such  a 
degree  of  heat  would  not  prove  that  another 
case  would  happen,  no  more  than  finding  forty 
thousand  clovers  bearing  three  leaves  only 
would  prove  that  clover  always  has  only  three 
leaves ;  or  finding  forty  different  varieties  of 
cloven-footed  animals  marked  with  horns  would 
prove  that  swine  must  have  horns.  But  now  I 
know  that  like  causes  will  produce  like  effects, 
and  I  know  also  by  observation  that  two  hund- 


ANALYTICAL  OUTLINE.  17 

red  and  twelve  degrees  Fahrenheit  did  once, 
or  twice,  or  thrice  cause  water  to  boil,  and  I 
therefore  infer  that  it  will  always  cause  water 
to  boil.  Admit  the  premises  and  the  conclusion 
is  unavoidable ;  and  to  do  this  is  simply  to 
affirm  something  of  a  class,  then  to  refer  an  in- 
dividual to  that  class,  and  then  to  affirm  the 
same  thing  of  that  individual. 

l^ow  the  first  premise  is  a  general  principle, 
which  is  intuitively  true.  The  only  question  is 
about  the  second  premise,  namely,  whether  two 
hundred  and  twelve  degrees  Fahrenheit  was  the 
cause  of  boiling  in  the  instances  observed. 

You  may  now  prove  this  by  another  argu- 
ment made  up  of  another  intuitive  principle, 
and  an  observed  fact,  or  perhaps  by  two  argu- 
ments, thus :  no  event  hapjpens  without  a  cause  / 
the  boiling  of  water  is  an  event,  therefore  it 
happened  not  without  cause ;  in  other  words,  it 
happened  by  some  cause.     What  cause? 

It  is  a  presumption  of  reason  that  those 
thvnqs  which  immediately  and  invariably  pre- 
cede a  certain  event  a/re  its  caMse^  or  include  its 
cause. 

Now  observation  and  experiment  have  shown 
when  two  hundred  and  twelve  degrees  Fahren- 


18  ELEMENTS    IF  LOGIC. 

heit  was  present  water  invariably  and  imme« 
diately  boiled ;  and  when  it  was  absent,  the 
other  circumstance  remaining  just  as  before,  it 
did  not  boil.  Hence  it  is  concluded  that  it  was 
the  cause  of  the  boiling  in  these  cases. 

Thus  the  second  premise  of  the  main  argu- 
ment being  proved,  the  first  conclusion  is  estab- 
lished, namely,  that  two  hundred  and  twelve 
degrees  Fahrenheit  is  always  the  cause  of  water 
boiling. 

Every  case  of  induction  proper  proceeds 
upon  the  same  grounds  and  in  the  same  way. 
It  is,  therefore,  evident  induction  is  no  excep- 
tion to  the  rule  that  inference  is  always  from 
generals  to  particulars,  and  not  from  particulars 
to  generals. 

8.  Reasoning  by  analogy  proceeds  in  the 
same  way ;  the  difference  is  only  in  the  char- 
acter of  the  first  premise,  which  is,  that  simila/r 
causes  are  likely  to  produce  similar  effects^  m 
that  things  which  agree  in  certain  attributes  oi 
relations  are  liJcely  to  agree  in  certain  other  at- 
ti'ibutes  or  relations.  Thus  we  reason  by  analo- 
gy that  Jupiter  is  likely  to  be  inhabited  as  well 
as  the  earth,  and  that  retribution  may  be  ex- 
pected in  a  future  life  as  well  as  in  this. 


ANALYTICAL  OUTLINE.  19 

%9.  Reasoning  a  jpriori  and  a  posteriori  are 
not  different  modes  of  reasoning,  but  arguments 
differing  in  the  character  of  one  of  the  premises : 
in  the  one  we  reason  from  antecedents,  and 
in  the  other  from  consequents.  From  the  idea 
of  perfection,  as  an  antecedent  in  the  human 
mind,  Des  Cartes  argued  a  priori  for  the  exist- 
ence of  a  Perfect  Being ;  and  Paley,  from  the 
marks  of  contrivance  in  the  world  as  an  effect, 
proved  a  posteriori  an  intelligent  Creator. 

10.  It  will  be  seen  that  the  value  of  any  con- 
clusion depends  upon  the  degree  of  certainty 
which  belongs  to  the  premise*.  If  they  are  cer- 
tain the  conclusion  is  certain ;  if  they  are  prob- 
able the  conclusion  is  only  probable  This  is 
the  only  distinction  between  mathematical  and 
moral  or  practical  reasoning ;  nor  does  this  al- 
ways exist,  for  some  moral  arguments  may  claim 
premises  that  are  absolutely  certain. 

11.  It  remains  only  to  observe  that  the  syl- 
logism is  merely  a  certain  convenient  mode  of 
stating  an  argument ;  and  that  is  the  most  per- 
fect syllogism  which  is  framed  so  as  to  make 
the  true  process  of  inference  the  most  apparent. 
The  above  instance  of  induction  would  be  stated 
as  a  syllogism,  thus: 


20  ELEMENTS  OF  LOGIC. 

like  canses  will  ever  produce  like  effects.  « 

Two  hundred  and  twelve  degrees  Fahrenheit  is  lik« 
the  canse  that  produced  boiling  of  water; 
Therefore,  it  will  ever  produce  the  like  effect 

Or  thus: 

Whatever  caused  the  boiling  of  water  once  will  always 
cause  it. 

Heat  212"  Fahrenheit  caused  the  boiling  of  water 
once; 

Therefore,  it  will  always  cause  it. 

12.  Analyzing  a  syllogism,  for  example: 

All  men  are  mortal. 
Mohammed  w<is  a  man ; 
Therefore,  Mohammed  was  mortal : 

we  find  that  it  is  made  up  of  three  propositions ; 
that  each  proposition  contains  two  terms  and  a 
copula,  expressing  an  agreement  or  disagreement 
of  the  terms.  Each  term  denotes  an  idea,  as  aU 
men^  mortal,  Mohammed;  each  proposition  ex- 
presses a  judgment  as  to  the  relation  of  two  terms 
to  each  other,  and  the  last  of  these  propositions 
is  an  inference  from  the  other  two  judgments. 
The  three  operations  of  mind  concerned  in  rea- 


ANALYTICAL  OUTLINE.  21 

Boning  are  therefore  simple  apprehension,  judg- 
ment, and  inference. 

13.  Language  serves  to  express  these  mental 
operations,  but  the  mind  has  ideas,  judgments, 
and  inferences  before  it  has  language,  inasmuch 
as  a  sign  must  of  necessity  be  subsequent  to  the 
thing  signified. 

14.  From  this  analysis  it  appears  that  logic 
enters  into  the  vital  processes  of  the  mind,  and 
conducts  it  from  the  known  to  the  unknown. 
A  demonstration  is  essentially  a  discovery :  the 
propositions  in  a  book  of  geometry  are  involved 
in  the  axioms  and  definitions  on  the  first  page, 
but  to  draw  them  out  is  as  much  a  discovery  to 
the  mathematician  as  the  continent  of  America 
was  to  Columbus. 


SYNTHESIS    OF    LOGIC; 


PART  I. 


OI^    TEEMS. 

1.  The  first  part  of  Logic  treats  of  Tekms. 

A  Term  is  one  or  more  words  expressing  a 
thing,  or  what  is  thought  of  a  thing ;  as, 

Chrass  is  green.  Grass  is  a  term,  and  green  is 
a  term. 

The  Sim  shmes  hrightly.  The  sun  is  a  term, 
and  shines  brighth/  is  a  term. 

SECTION   I. 

DIFFEEENT   KINDS   OF   TERMS. 

2.  A  Singular  Term  expresses  only  one  indi- 
vidual; as, 

Boston^  Connecticut  River,  this  rock,  the  discoverer  of 
America. 

*  Younger  students  corAnience  here. 


24  ELEMENTS  OF  LOGIC 

3.  A  Common  Term  is  one  whicli  is  not  con- 
lined  to  a  single  object,  as  Gity^  which  may 
apply  to  Boston  and  to  all  other  cities. 

Rock,  River,  Conqueror,  Mariner. 
Strong,  Happy,  Wise,  Great,  Balmy,  Dark. 

4.  A  Relative  Teem  expresses  an  object 
that  is  related  to  another  object ;  as,  Husband^ 
which  is  related  to  wife.  Pa/rent^  which  im- 
plies offspring. 

Rider,  Rnler,  Brother,  Servant,  Magistrate. 

6.  An  Absolute  Term  expresses  a  thing  con- 
sidered by  itself,  without  reference  to  any  other 
thing;  as, 

River,  Mountain,  Power,  Wisdom. 

6.  A  Positive  Term  expresses  a  thing  as 
actually  existing;  as. 

Sight,  Seeing,  Speech,  A  man  speaking. 

7.  A  Privative  Term  is  one  which  expresses 
the  absence  of  an  attribute  from  a  thing  capable 
of  it;  as,  a  blind  man^  which  denotes  the  ab- 
sence of  the  power  to  see. 

A  lame  stag,  A  leafless  oak,  A  dead  plant. 


DIFFERENT  KINDS  OF  TERMS.  26 

8.  A  Negative  Term  denotes  the  absence 
of  an  attribute  from  a  subject,  which  is  not 
capable  of  it  at  all ;  as, 

A  dumb  statue,  Lifeless  marble,  Silent  dews. 

9.  An  Abstract  Term  is  one  which  ex 
presses  a  quality,  without  reference  to  any 
subject  in  which  it  may  be  found ;  as. 

Roundness,  Hardness,  Wisdom,  Justice,  Folly. 

10.  A  Concrete  Term  expresses  both  the 
attribute  and  the  object  to  which  it  belongs ; 
as,  wrong^  which  expresses  both  an  action  and 
its  quality ;  i^ler^  which  indicates  an  agent  and 
his  office. 

Philosopher,  Governor,  Wise,  Energetic,  Hard. 

11.  An  Indefinite  Term  is  one  which  does 
not  define  or  mark  out  an  object,  and  has  the 
particle  not  attached  to  it,  expressed  or  under- 
stood; as,  not  a  mem,  which  may  imply  any 
other  being. 

Not  Brutus,  Incorporeal,  Unfinished,  Unwise 


26  ELEMENTS  OF  LOGIC. 

12.  A  Definite  Term  is  one  which  does  de- 
fine or  mark  out  an  object  and  has  not  the 
particle  not  attached  to  it ;  as, 

Man,  Brutus,  Finished,  Complete,  Established. 

EXAMPLES. 

1.  Man  is  a  rational  being. 

2.  Cicero  was  a  great  orator. 

3.  This  town  is  pleasantly  situated. 

4.  Mothers  have  much  solicitude. 

5.  Strength  is  acquired  by  exercise. 

6.  Far-sightedness  is  peculiar  to  seamen. 
T.  A  dumb  man  is  a  pitiful  object. 

8.  The  silent  tomb,  the  lifeless  statue. 

9.  Wisdom  is  more  precious  than  rubies. 

10.  Just  and  good  are  the  laws  of  God. 

11.  The  society  is  organized. 

12.  The  plan  is  incomplete. 

SECTION  n. 

OPPOSITION   OF   TERMS. 

13.  Consistent  Teems  are  those  which  may 
at  the  same  time  be  affirmed  of  the  same  thing; 
as,  dry  and  cold. 


OPPOSITION  OF  TERMS.  27 

14.  Opposite  Terms  cannot  at  the  same  time 
be  affirmed  of  the  same  thing;  as,  black  and 
white. 

The  opposition  of  terms  is  fourfold. 

15.  Relative  Opposition  is  that  w^hich  is  be- 
tween relative  terms,  that  cannot  at  the  same 
time  be  applied  to  the  same  subject;  as,  father 
and  son, 

16.  CoNTEABY  Opposition  is  that  between 
absolute  terms,  that  expel  one  another  from  a 
subject  capable  of  either ;  as,  wise  and  foolish. 

IT.  Privative  Opposition  is  that  between  a 
positive  and  privative  term ;  as,  seeing  and 
hlind. 

18.  Contradictory  Opposition  is  that  be- 
tween a  definite  and  indefinite  term ;  as  Cesa/r 
and  not  Cesa/r. 


EXAMPLES. 

1.  Good  and  small. 
2   Master  and  servant. 

3.  Ruler  and  subject. 

4.  Material  and  immaterial. 

5.  Lovely  and  hateful. 

6.  Hearing  and  deaf. 


28  ELEMENTS  OF  LOGIC. 

SECTION   III. 

SPECIES   AND    GENUS. 

This  subject  involves  no  mystery,  as  lormerly 
under  a  false  philosophy. 

19.  Species  is  a  term  that  denotes  a  class,  in- 
cluding several  individuals ;  as,  Beast,  which  in- 
cludes the  horse,  cow,  lion,  deer,  etc. 

20.  Genus  is  a  term  that  denotes  a  class,  that 
includes  several  species ;  as  Animal,  which  in- 
cludes beast,  bird,  fish,  man,  insect. 

A  genus  which  cannot  be  comprehended 
under  a  higher  genus  is  called  highest  geniis^ 
and  a  species  which  includes  no  lower  species 
is  called  lowest  species, 

21.  The  Essential  Difference  denotes  an 
essential  part  of  a  species  that  distinguishes  it 
from  other  species ;  as  rational,  which  is  the 
essential  difference  of  the  species  man,  because 
it  is  the  essential  part  of  man  that  distinguishes 
him  from  beast,  bird,  etc. 

22.  A  Property  is  something  necessarily 
joined  to  the  essential  difference ;  as  jpower  of 
laughing,  which  is  the  property  of  man  as  a 
rational  being. 


SPECIES  AND  GENUS.  29 

23.  An  Accident  is  something  that  may  be, 
or  may  not  be  joined  to  the  essential  difference, 
as  tall  or  shorty  li/vrng  in  London^  horn  in 
Paris, 

EXAMPLES 

1.  This  tree  is  a  Pine,  with  very  thick 
boughs. 

2.  This  is  a  small  magnet,  having  the  power 
of  attraction,  and  it  turns  upon  a  pivot  in  a 
direction  north  and  south. 

3.  This  vessel  is  a  ship,  having  three  masts, 
full  rigged,  and  very  long. 

4.  A  republic  is  a  government  in  which  the 
people  have  sway  and  choose  their  own  rulers. 

5.  This  seminary  of  learning  is  a  college. 

6.  A  lame  animal,  a  blind  stag. 

7.  General  terms  are  names  of  classes. 

8.  A  bird  with  blue  feathers  and  broad 
wings 

9.  Mercury  is  the  planet  nearest  the  Hun. 

10.  A  circle  is  a  figure  whose  circumference 
is  in  every  part  equally  distant  from  the 
center. 

11.  A  whale  is  the  largest  of  fish,  and  is 
often  seen  in  our  waters. 


80  ELEMENTS  OF  LOGIC. 

12.  A  plant  is  an  organized  being,  destitute 
of  sensation. 


SECTION  IV. 

DIVISIOIT. 

24.  Division  is  the  distinct  enumeration  of 
the  several  things  signified  by  a  term ;  as, 

New  England  is  divided  into  Maine,  New  Hampshire, 
Vermont,  Massachusetts,  Rhode  Island,  and  Connecticut. 

Bark  signifies  the  rind  of  a  tree,  a  small  ship,  and  the 
cry  of  a  dog. 

25.  EuLE  OF  Division.  The  several  parts  must 
not  he  contained  m  one  another,  and  all  to* 
gether  must  he  exactly  equal  to  the  thmg 
divided. 

EXAMPLES.* 

1.  The  year  is  divided  into  Summer, 
Autumn,  Winter,  and  Spring. 

2.  Metals  are  divided  into  gold,  copper,  and 
iron. 

3.  The  Human  race  is  divided  into  Ameri- 
cans,  Africans,  Asiatics,  Chinese,  and  Europeans. 

♦  Examples,  it  will  be  seen,  are  given  for  cr -ticiBm. 


DEFINITION.  91 

4.  King  signifies  a  ruler  and  also  a  man's 
Aamc. 

6.  Mercury  is  the  name  of  a  heathen  deity, 
a  planet,  a  plant,  and  quicksilver. 

6.  The  globe  consists  of  land  and  water. 

7.  Form  signifies  shape  and  ceremony. 

8.  Trump  is  a  trumpet  and  a  winning  card. 

9.  Orchard  is  an  inclosure  for  apple-trees 
and  fruit-trees. 

10.  A  solid  body  has  length  and  breadth. 

11.  A  tree  consists  of  trunk,  branches,  and 
leaves. 

SECTION  Y. 

DEFINITION. 

26.  A  Definition  is  an  expression  explaining  a 
term,  so  as  to  distinguish  or  separate  it  from 
everything  else. 

27.  A  Nominal  Definition  distinguishes  the 
meaning  of  a  term  by  an  equivalent  term, 
wliich  is  better  known ;  as, 

Decalogue — ^the  Ten  Oommandments. 

When  all  the  equivalent  terms  are  given  it  is 
one  kind  of  division. 


82  ELEMENTS  OF  LOGIC. 

28.  A  PnrsioAL  Definition  lays  down  the 
real  parts  of  the  essence  ;  as, 

Injustice  is  the  intentional  violation  of  another's  rights. 
A  plant  has  leaves,  stalks,  roots. 

This  last  is  another  kind  of  division. 

29.  A  Logical  Definition  assigns  the  Genus 
and  the  Essential  Difference  of  the  thing  de- 
fined; as, 

Man  is  a  rational  animal. 

30.  Accidental  Definition,  or  Description, 
assigns  the  accidents  or  properties  of  the  thing 
defined ;  as, 

Man  is  an  animal  that  uses  fire  to  dress  his  food. 
Columbus  was  a  native  of  Genoa. 

31.  It  will  be  observed  that  more  than  one 
of  these  kinds  of  definition  will  coincide  in 
matters  strictly  scientific. 

32.  Rule  of  Definition.  A  Definition  mvM 
be  adequate^  that  is^  not  too  extensive  nor  too 
narrow^  for  the  thing  defim^ed;  plainer^  and 
contained  in  a  suitable  number  of  proper^  not 
f-gurative  terms. 

33.  The  chief  concern  of  Logic  with  defini 


DEFINITIONS.  88 

tions  is,  that  words  be  not  used  in  differmi 
senses  in  argument. 

EXAMPLES. 

1.  Pleiades — the  seven  stars. 

2.  A  king  is  the  ruler  of  a  people. 

3.  A  square  is  a  figure  having  four  sides  and 
four  right  angles. 

4.  Surprise  is  a  state  of  mind  produced  by 
some  unexpected  occurrence. 

6.  A  circle  is  a  figure  whose  circumference 
is  in  every  point  equally  distant  from  the 
center. 

6.  Species  is  a  term  for  a  class. 

7.  Wine  is  the  juice  of  the  grape. 

8.  Whiteness  is  the  color  arising  from  the 
prevalence  of  brightness. 

9.  A  plant  is  an  organized  being  destitute  of 
sensation. 

10.  Logic  is  the  science  of  infeience. 

11.  Man  is  a  risible  animal. 

12.  Mercury  is  the  planet  nearest  the  Sun. 

13.  A  Church  is  a  congregation  of  faithful 
men,  in  which  the  word  of  God  is  preached, 
and  the  ordinances  duly  administered. 


84  ELEMENTS  OF  LOGIC 

14:.  Punishment  is  pain  inflicted  for  a  crime, 
in  order  to  correct  the  offender. 

15.  Courage  is   boldness  and  endurance  in 
time  of  peril. 

16.  Sin  is  voluntary  transgression  of  a  known 
law. 

17.  Sin  is  any  transgression  of  God's  law. 


PART  !!• 


OF   PEOPOSITIONS. 

The  second  part  of  Logic  treats  of  Propo 
Bitions. 

SECTIOK  I. 

1.  A  Proposition  is  a  judgment  expressed 
in  words,  or  a  sentence,  whereof  one  part 
is  affirmed  or  denied  of  the  other ;  as, 

Man  is  an  animal. 

Moses  and  Thomas  are  not  Statesmen. 

All  animals  are  mortal. 

2.  The  Subject  of  a  proposition  is  that  part, 
of  which  something  is  affirmed  or  denied ;  as, 
in  the  last  example  all  animals  is  the  subject. 

3.  The  Predicate  of  a  proposition  is  that 
which  is  affirmed  or  denied  of  the  subject;  as, 
in  the  same  example,  mortal  is  the  predicate. 


B6  ELEMENTS  OF  LOGIC. 

4.  The  Copula  is  the  verb  by  which  the 
two  terms  are  connected.  It  is  the  present  tense 
of  the  verb  to  he,  with  or  without  the  particle  not. 

5.  Sometimes  one  part  of  a  proposition  is 
contained  in  another;  as,  the  wind  blows,  I 
think,*  which  imply,  /  am  thinking,  the  wind  is 
Mowing. 

6.  The  subject  of  a  proposition  usually 
stands  first,  and  the  predicate  last;  but  this 
order  is  sometimes  inverted,  as. 

In  the  West  are  extensive  Prairies. 

EXAMPLES. 

1.  Matter  is  divisible. 

2.  Man  is  not  infallible. 

3.  Christopher  Columbus  was  the  discoverer 

of  America. 

4.  A  wise  man  rules  his  own  spirit. 

6.  George  Washington  was  a  brave  but  pru- 
dent general. 

6.  The  world  exhibits  marks  of  a  great  con- 

vulsion. 

7.  I  see — he  feels — ^you  w^alk — they  run. 

8.  All  tyrants  deserve  death. 

9.  Blessed  are  the  pure  in  heart. 


DISTINCTION   OF  PROPOSITIONS.  37 

SECTION  II. 

DISTIKOTION   OF   PROPOSITIONS. 

7.  Pbopositions  are  distinguished  into  af- 
firmative and  negative,  which  is  a  distinction 
with  respect  to  Quality. 

8.  An  Affirmative  Proposition  is  one  in 
which  the  predicate  is  declared  to  agree  with 
the  subject;  as, 

Man  is  a  fallible  oreatnre. 

9.  A.  Negative  Proposition  is  one  m  whicli 
the  predicate  is  declared  to  disagree  with  the 
subject;  as, 

The  world  is  not  eternal ;  no  miser  is  happy. 

10.  Propositions  are  also  distinguished  into 
iJniversal  and  Particular,  which  is  a  distinc- 
tion in  respect  to  Quantity. 

11.  A  Universal  Proposition  is  one  in  which 
the  predicate  is  asserted  of  the  whole  of  the 
subject. 

The  signs  of  universality  are  all^  every,  no, 
neither,  and  the  like,  which  are  expressed  or 


38  ELEMENTS  OF   LOGIC. 

understood  ;  also,  proper  names,  as  John,  Lon- 
don ;  and  common  names  with  a  singular  or 
a  definite  sign  ;  as,  That  hoy^  five  hoohs, 

No  discontented  man  is  happy. 
Those  stars  revolve  about  the  sun. 

Exceptions.  In  negative  propositions  the 
idiom  of  the  English  language  makes  all  and 
eoery  particular  or  singular  terms;  as,  all  tJie 
sailors  were  not  drowned^  does  not  mean  that  all 
the  sailors  escaped  drowning,  but  that  some  of 
them  only  escaped  drowning ;  or,  it  denies 
drowning  of  the  totality  as  a  collective  unit. 

To  state  a  universality  here  you  must  say: 
None  of  the  sailors  were  drowned^  or  simply, 
The  sailors  were  not  drowned, 

12.  A  Particular  Proposition  is  one  in 
which  the  predicate  is  asserted  of  an  indefinite 
part  of  the  subject. 

The  signs  of  particularity  are  some^  many, 
few^  several,  and  the  like ;  as, 

Some  culprits  were  not  punished. 

13.  A  Universal  Affirmative  Proposition 
is  one  in  which  the  predicate  is  said  to  agree 


DISTINCTION  OF  PROPOSITIONS.  S9 

with  the  whole  of  the  subject ;  as,  in  the  above 
example — All  men  are  mortal.  This  is  not  only 
a  universal  proposition,  but  a  universal  affirma- 
tive proposition. 

All  tyrants  deserve  death. 

14.  A  Universal  Negative  Proposition  is 
one  in  which  the  predicate  is  said  to  disagree 
with  the  whole  of  the  subject;  as,  no  disoon 
tented  man  is  happy j  which  is  not  only  a  uni- 
versal proposition,  but  a  universal  negative 
proposition. 

No  sins  are  excusable. 

15.  A  Particular  Affirmative  Proposition 
is  one  in  which  the  predicate  is  asserted  to 
agree  with  only  some  part  of  the  subject;  as,  sorihe 
islands  are  fertile*  which  is  not  only  a  par- 
ticular proposition,  but  a  particular  affirmative 
proposition. 

Several  men  were  drowned. 

16.  A  Particular  Negative  Propodiiion  is 
one  in  which  the  predicate  is  asserted  to  dis- 
agree with  only  some  part  of  the  subject ;  as,  some 
culprits  were  not  pimished;  which  is  not  only 


4:0  ELEMENTS  OF  LOGIC. 

a  particular  proposition,  but  a  particular  nega 
tive  proposition. 

17.  A,  E,  I,  O  are  symbols  employed  to  re- 
present these  propositions :  thus, 

A  stands  for  universal  affirmative. 

E  stands  for  universal  negative. 

I   stands  for  particular  affirmative. 

O  stands  for  particular  negative. 

EXAMPLES. 

1.  These  sailors  were  not  drowned. 

2.  Paris  is  a  gay  city. 

3.  Some  animals  are  sagacious. 

4.  Men  are  unaccountable  beings. 

5.  Every    effect    must    have    an    adequate 

cause. 

6.  Few  men  become  suddenly  rich. 

7.  Many  criminals  are  not  brought  to  pun- 

ishment. 

8.  Planets  are  bodies  moving  in  orbits  about 

the  sun. 

9.  Islands  are  surrounded  by  water. 

10.  The    Christian    religion    is    attested    by 

miracles. 

11.  Every  sinner  will  be  punished. 


DISTINCTIONS  OF  PROPOSITIONS.  41 

12.  That  man  was  the  inventor  of  lightning 

rods. 

13.  Not  all  his  foes  could  alarm  him. 

14.  No  flower  is  always  in  bloom, 

15.  All  laws  are  not  useful. 

16.  Every  soldier  was  not  killed. 


SECTION  III. 

FURTHER   DISTINCTIONS    OF   PROPOSITIONS. 

18.  Propositions  are  distinguished  into  Cate- 
gorical and  Hypothetical. 

19.  The  Categorical  asserts  simply  that  the 
predicate  agrees  or  disagrees  with  the  sub- 
ject; as, 

Truth  is  invaluable. 

The  eye  is  a  natural  telescope. 

20.  The  Hypothetical  asserts  with  a  con- 
lition,  or  with  an  alternative ;  as, 

If  it  storms,  the  ship  will  not  saiL 
It  is  summer  or  winter. 

21.  Hypothetical  Propositions  are  divided 
into  Conditional  and  Disjunctive. 


42  ELEMENTS   OP  LOGIC. 

22.  A  Conditional  Proposition  is  one  whose 
parts  are  limited  by  the  particle  if^  or  some 
word  expressing  a  condition ;  as, 

If  there  be  no  fire,  there  will  be  no  heat. 
Cesar  deserved  death,  if  he  was  a  tyrant. 

23.  A  Conditional  Proposition  contains  two, 
and  only  two,  Categorical  Propositions,  whereof 
one  follows  from  the  other. 

If  the  Bible  is  true,  it  ought  to  be  studied. 

The  first  is  called  the  antecedent,  and  that 
which  results  from  it  is  called  the  consequent. 

24.  A  DisjuNcnvE  Proposition  asserts  that 
a  subject  agrees  with  one  of  two  or  more  pred- 
icates, or  a  predicate  with  one  of  two  or  more 
subjects;  as, 

It  is  either  day  or  night. 

Prosperity  or  adversity  wiU  be  yonr  lot. 

25.  A  Disjunctive  may  easily  be  converted 
j.nto  a  Conditional ;  thus, 

It  is  either  day  or  night. 
K  it  is  not  day,  it  is  night. 


TERMS  OF  PROPOSITIONS.  48 

EXAMPLES. 

1 .  Man  is  free,  or  he  is  not  responsible. 

2.  This  proposition  is  either  true  or  false. 

3.  The  earth  must  move,  if  the  sun  be  fixed. 

4.  If  the  harvest  is  large,  corn  will  be  cheap. 
6.  If  there  be  no  providence,  prayer  avails  not. 

6.  If  the  boat  goes,  the  letter  will  probably 

reach  him  before  morning. 

7.  Wisdom  is  the  principal  thing,  if  Solomon 

is  right. 

8.  Either  the  sun  or  the  moon  will  be  eclipsed 

that  day. 

9.  If  logic  is  useful,  it  deserves  to  be  studied. 
10.  If  Cromwell  was  an  Englishman,  he  was 

a  usurper. 

SECTION  lY. 

DISTRIBUTION     OF    THE    TERMa    OF    PROPOSI- 
TIONS. 

26.  A  Term  is  said  to  be  distributed  when  it 
is  taken  universally  or  in  its  utmost  extent,  so 
as  to  stand  for  everything  to  which  it  is  capable 
of  being  applied,  that  is,  for  each  of  its  signifi- 
cates ;  and  undistributed  when  it  stands  for  an 


4:4  ELEMENTS  OF    LOGIC. 

indefinite  portion  only  of  the  things  signified 
by  it,  that  is,  for  an  indefinite  part  of  a  class. 
In  the  following  example  the  subject  is  dis- 
tributed and  the  predicate  undistributed. 

All  birds  are  animals. 

In  the  following  the  predicate  is  distributed 
and  the  subject  undistributed. 

Some  birds  are  not  web-footed. 

It  is  evident  that  the  whole  class  of  web- 
footed  are  separated   by   the  not  from  some 

birds. 

RULE  I. 

27.  Subjects  are  distributed  in  all  uni/versal 
a/ad  no  jpa/rticula/r  propositions. 

All  men  are  mortal. 
Great  Britain  rules  the  ocean. 
Wicked  men  are  not  wise. 
The  fixed  stars  twinkle, 
No  miser  is  a  happy  man. 

RULE  n. 

28.  Predicates  are  distributed  in  all  ntigattve 
and  no  affirmative  propositions. 

No  virtue  is  an  evil. 

Some  rich  men  are  not  good  men. 


TERMS  OF  PROPOSITIONS.  46 

A  distributes  the  subject,  O  the  predicate,  I 
neither,  and  E  both. 

N.  B. — A  defini'-e  portion  of  a  class  is  a  small 
class,  and  the  term  which  expresses  it  is  dis- 
tributed. 

Most  men  are  poor. 
These  men  are  rich. 

Eule  II  has  some  Exceptions  in  what  logi- 
cians call  tmnatmral  jyroposiUonSj  such  as, 

All  triangles  are  all  figures  bounded  by  three  straight 
lines. 
Some  stars  are  all  the  planets. 
Some  stars  are  not  some  planets. 

But  these  being  noted  by  the  form  of  ex- 
pression will  make  no  difficulty. 

I  do  not  see  with  Sir  William  Hamilton  suffi- 
cient reason,  in  such  exceptions,  to  revolutionize 
ihe  established  forms  of  logic. 

EXAMPLES. 

1.  Many  ships  were  lost  in  the  gale. 

2.  The  storm  did  not  last  long. 

3.  Most  Americans  can  read. 

4.  All  the  laws  were  not  enforced. 


46  ELEMENTS  OF  LOGIC. 

5.  Everything  in  the  political  world  looks 

dark. 

6.  "No  good  man  can  hate  his  brother. 

7.  Every  sin  is  a  violation  of  the  divine  law. 

8.  All  visible  things  had  a  beginning. 

9.  Some  difficult  things  are  not  evils. 

10.  Charity  never  faileth. 

11.  Charity-  suffereth  long  and  is  kind. 

12.  Five  men  were  shipwrecked, 

SECTION  Y. 

OPPOSITION   OF   PROPOSITIONS. 

29.  Two  propositions  are  said  to  be  opposed, 
which,  having  the  same  subject  and  predicate, 
yet  differ  in  quantity,  or  quality,  or  both ;  as, 


A.  All  islands  are  fertile, 
I.  Some  islands  are  fertile 


.,     >•  m  quantity, 
lie,  )       ^ 

A.  All  islands  are  fertile,   )  . 

>  m  cinahty. 
E.  No  island  is  fertile,       J      ^       ^ 


A.  All  islands  are  fertile,  ,  .    ,    .. 

Y  in  both. 
O.  Some  islands  are  not  fertile, 


E.  No  island  is  fertile,        r  .    ,     , 

Y  m  both. 
I,   Some  isl  ands  are  fertile, 


iile,  ) 
bUe,  ) 


OPPOSITION  OF  PROPOSITIONS.  47 

30.  With  any  given  subject  and  predicate, 
four  distinct  propositions  may  be  stated,  namely, 
A,  E,  I,  and  O,  any  two  of  which  may  be  said 
to  be  opposed  ;  as. 


Or, 


A.  Every  disease  is  contagious. 
E.  No  disease  is  contagious. 

I.    Some  diseases  are  contagious. 
O.  Some  diseases  are  not  contagious. 


31.  There  are  four  different  kinds  of  opposi- 
tion. 

32.  Contrary  Opposition  is  when  a  uni- 
versal affirmative  is  opposed  to  a  universal 
negative;  as, 

A.  All  human  inventions  are  perfect. 
E.  No  human  invention  is  perfect. 

33.  SuBCONTRARY  OPPOSITION  IS  wlieu  the 
particular  affirmative  is  opposed  to  the  particu- 
lar negative ;  as, 

I.  Some  human  inventions  are  perfect. 
0.  Some  human  inventions  are  not  perfect. 

34.  Subaltern  Opposition  is  when  a  univers- 
al affirmative  is  opposed  to  a  particular  affirm- 


48  ELEMENTS  OF    LOGIC. 

ative,  or  a  universal  negative  to  a  particular 
negative;  as, 

A.  Every  human  invention  is  perfect 
I.    Some  human  inventions  are  perfect. 

Or, 

E.  No  human  invention  is  perfect. 

0.  Some  human  inventions  are  not  perfect. 

35.  OoNTRADioTORY  OpposnioN  is  wheu  the 
universal  affirmative  and  the  particular  negative 
are  opposed,  or  the  universal  negative  and  the 
particular  affirmative;  as, 


Or, 


A.  Every  human  invention  is  perfect. 

O.  Some  human  inventions  are  not  perfect, 

E.  No  human  invention  is  perfect. 
L   Some  human  inventions  are  perfect. 


36.  Four  conditions  are  requisite  to  consti- 
tute a  contradiction,  namely,  to  speak  of  the 
same  thing :  (1.)  In  the  same  sense ;  (2.)  In  the 
same  respect;  (3.)  With  regard  to  the  same 
third  thing;  and,  (4.)  At  the  same  time.  If  any 
of  these  be  wanting,  is  and  is  not  may 
agree.    As, 


OPPOSITION   OF  PROPOSITIONS.  49 

1.  An  opinion  is  and  is  not  faith*  It  is  an 
inoperative  and  unacceptable  belief;  it  is  not 
an  effectual  and  saving  faith.  2.  Troilus  is 
wnd  is  not  red-haired.  He  is  with  respect  to 
Lis  head ;  he  is  not  with  respect  to  his  beard 
3.  Socrates  is  and  is  not  long-haired^  he  is  in 
comparison  with  Scipio ;  he  is  ot  in  compari- 
son with  Xenophon.  4.  Solomo\  was  and  was 
not  a  good  man.  He  was  in  his  youth ;  he  was 
not  in  his  middle  age. 

THE   RULES   OF   OPPOSITION, 
RULE   L 

37.  Coin-RADioTORY  Propositions  are  always 
the  one  true  and  the  other  false ;  as, 

A.  All  men  are  mortal. 

0.  Some  men  are  not  mortaL 

E.  No  tyrant  deserves  death, 

1,  Some  tyrants  deserve  death. 

RULE  n. 

38.  Contrary   Fropositionb    may   be   both 

false,  but  never  both  true  ;  as, 
4 


60  ELEMENTS  OP   LOGIO. 

A.  Every,  disease  is  contagions. 
E.  No  disease  is  contagions. 

BULE  nL 

39.  SuBooNTRABiES  are  never  both  false,  but 
tliey  may  be  both  true. 

I.   Some  jminsements  are  innocent. 
0.  Some  amnsements  are  not  innocent. 

RULE  IV. 

40.  Subalterns  are  sometimes  both  true, 
sometimes  both  false,  and  sometimes  one  is  true 
and  the  other  false ;  as, 

A.  Every  defensive  war  is  jnst, 
L  Some  defensive  wars  are  just. 
E.  No  crime  is  an  evil. 

0.  Some  crimes  are  not  an  evil. 

A.  Every  measure  of  government  is  wise. 

1.  Some  measures  of  government  are  wise. 

A^- Contraries' 

Diagram  showing  the         N. 

I       \ 
relation  of  the  four  judg-    ©  %-^^ 

ments-.AEIO.  S      X       S 


x^- — s 


Subcontraries- 


OPPOSITION  OF   PROPOSITIONS.  61 

EXAMPLES. 

1.  Some  horses  are  unruly. 
Some  horses  are  not  unruly. 

2.  No  intolerant  men  are  good  men. 
Some  intolerant  men  are  good  mea 

3.  All  pleasures  are  hurtful. 
Some  pleasures  are  not  hurtful. 

4:.  All  hopes  are  consoling. 
Some  hopes  are  consoling. 

5.  No  virtuous  man  is  ungrateful. 
Some  virtuous  men  are  ungrateful 

6.  All  islands  are  fertile. 
Some  islands  are  fertile. 

T.  All  animals  are  mortal. 
All  animals  are  not  mortal. 

8.  Every  patriot  is  a  Christian. 
Some  patriots  are  not  Christians. 

9.  Some  diseases  are  contagious. 
All  diseases  are  contagious. 

iO.  All  laws  are  not  useful. 
Some  laws  are  not  useful. 


62  ELEMENTS  OF  LOGIC. 

SECTION  VI. 

CONVERSION   OF   PROPOSITIONS. 

41.  A  proposition  is  said  to  be  converted, 
when  its  terms  are  transposed  and  the  truth 
preserved ;  as, 

Some  painters  are  poets. 
Some  poets  are  painters. 

42.  The  proposition  to  be  converted  is  called 
the  Original,  that  into  which  it  is  converted 
the  Converse  ;  as. 

Original.    No  reptile  is  a  quadruped. 
Converse.    No  quadruped  is  a  reptile. 

43.  Simple  Conversion  is  where  the  subject 
and  predicate  simply  change  places ;  as, 

Some  boasters  are  cowards. 
Some  cowards  are  boasters. 

44.  Particular  Conversion  is  where,  in 
transposition,  the  converse  requires  a  particular 
term  to  preserve  the  truth  of  the  original ;  as, 

All  swallows  are  birds. 
Some  birds  are  swallowa. 


CONVERSION  OF  PROPOSITIONS.  58 

45.  Rule.  In  all  cases  the  converse  muat  he 
timly  implied  hy  the  original^  and  no  tenn 
must  he  distributed  in  the  converse  that  was  not 
distributed  in  the  original.     Hence, 

A.  All  men  are  mortal ; 
All  mortals  are  men, 

is  not  proper  conversion,  for  A  distributes  the 
subject  only,  (28)  but  mortal  is  the  predicate, 
therefore  its  distribution  in  the  converse, 
namely,  all  mortals^  is  unwarranted. 

46.  The  converse  of  a  universal  affirmative 
proposition  is  a  particular  affirmative ;  or,  more 
briefly,  A  is  converted  into  I. 

A.  All  men  are  mortal. 
I.    Some  mortals  are  men, 

47.  The  converse  of  a  universal  negative  is  a 
universal  negative — E  into  E ;  as, 

E.  No  deer  is  an  elephant. 
E.  No  elephant  is  a  deer. 

48.  Particular  affirmative  propositions  are 
converted  only  into  the  same — I  into  I;  as, 

I.  Some  infidels  are  learned  men. 
I.  Some  learned  men  are  infidels. 


54  ELEMENTS  OF    LOGIC. 

49.  A  particular  negative  is  inconverti- 
ble; as, 

0.  Some  birds  are  not  swallowrs. 

You  cannot  say, 

0.  Some  swallows  are  not  birds; 

Or, 

E.  No  swallows  are  birds ; 

For  these  are  negative  propositions,  and  dis- 
tribute the  predicate,  (28)  which  is  hirds;  but, 
in  the  original,  hirds^  is  not  distributed.  (27.) 

Some  logicians  teach  that  the  particular 
negative  may  be  converted  by  considering  the 
particle  not  attached  to  the  predicate,  by  which 
the  proposition  is  taken  as  an  affirmative. 

Some  statesmen  are  not  wise^  may  be  stated  . 

Some  statesmen  are  not- wise. 
This  you  may  convert  simply: 

Some  not-wise,  that  is,  unwise,  are  statesmen. 

In  like  manner  a  universal  affirmative  may 

be  simply  converted  by  changing  its  quah'ty; 

thus, 

All  good  reasoners  are  candid  men, 

may  be  converted  into 

None  but  candid  men  are  good  reasonera 


CONV'jflRSION  OF  PROPOSITIONS.  65 

This  is  called  conversion  bj  contraposition. 

50.   Exceptions.    Universal  affirmatives  may 

be    converted   simply  when   the   predicate  by 

some  word  notifies  its  distribution,  contrary  to 

rule,  sec.  iv,  28,  and  when  it  is  understood  to  be 

exactly  equal  to  the  subject,  as  in  definitions, 

etc. 

All  men  are  [aU]  rational  animals. 

So  some  particular  negative  proposition  ma^ 
be  converted  simply  when  the  predicate  notifies 
its  non-distribution.  See  exceptions  to  Kule  II, 
Sec.  iv,  28. 

Some  elms  are  not  some  trees. 

EXAMPLES. 

1.  All  Britons  are  freemen. 

2.  Some  Britons  are  freemen. 

3.  No  unhappy  man  is  a  perfect  Christian. 

4.  Some  fish  are  not  salmon. 

5.  Some  orators  are  not  statesmen. 

6.  No   offensive  wars    are  righteous  ente^ 

prises. 

7.  Every  learned  man  is  a  thankful  man. 

8.  Some  great  geniuses  are  ignorant  meiL 

9.  Some  parrots  are  not  talkers. 


66  ELEMENTS  OF   LOGIC. 

10.  Every  true  Christian  is  a  patriot. 

11.  Some  angels  are  sinners. 

12.  Some  amusements  are  hurtful. 

13.  All  birds  have  feathers  and  wings. 

14.  All  equiangular  triangles  are  equilateral 

15.  Some  stars  are  all  the  planets. 

16.  Some  stars  are  not  some  planets. 

17.  A  few  men  are  not  all  the  voters. 

18.  Some  birds  are  not  like  some  birds. 


PART  III. 


OF   AEGTJMENT. 

1.  The  third  part  of  Logic  treats  of  Argxt 
ment,  or  reasoning  expressed  in  words. 

2.  An  Argument  is  an  expression  in  which, 
from  something  laid  down  and  granted  as  true, 
something  else  beyond  this  mnst  be  admitted  to 
be  true,  as  following  necessarily  from  the  other. 
That  which  is  laid  down  is  called  the  Premises, 
that  which  results  therefrom  is  called  the  Con- 
clusion. 

3.  Every  valid  argument  must  conform  to 
the  Logical  axiom,  that  being  the  only  prin- 
ciple on  which  all  reasoning  proceeds,  namely: 

Whatever  is  universally  affirmed  or  denied  of  a 
class,  may  be  affirmed  or  denied,  in  like  manner^ 
of  everything  comprehended  in  that  class. 

Or,  as  stated  by  Aristotle,  and  hence  called 
Aristotle's  dictum : 


68  ELEMENTS  OF  LOGIC. 

Whatever  is  predicated  of  a  term  disi/i'lhuted 
ma/y  he  predicated  in  lihe  manner  of  every- 
thing contaimed  in  it.    As, 

All  tyrants  deserve  death ; 

Oesar  was  a  tyrant; 

Therefore  Oesar  deserved  death. 

No  man  enslaved  by  appetite  can  be  happy ; 
The  sensualist  is  enslaved  by  appetite ; 
Therefore,  no  sensualist  can  be  happy. 


SECTION  I. 

OF     SYLLOGISM. 

4.  An  argument  stated  at  full  length  and  in 
its  regular  form  is  a  Syllogism.  The  above 
examples  are  syllogisms. 

5.  Every   regular  syllogism  contains  three, 

and  only  three  terms,  called  the  Minor  term, 

Major  term,  and  Middle  term. 

•* 
All  tyrants  deserve  death, 
8  2 

Cesar  was  a  tyrant^ 

1  8 

Therefore,  Gesa/r  deserved  death 


OF  SYLLOGISM.  59 

6.  The  subject  of  the  conclusion  is  the  minor 
l,erm ;    the  predicate  of  the  conclusion  is  the 

.major  term ;  and   the   other  term   with  which 
these  are  compared  is  the  middle  terra  ;  as, 

All  tyrants  deserve  death ; 

MlddU. 
Cesar  was  a  tyrant ; 

Minor.  Major. 

Therefore  Cesar  deserved  death. 

The  predicate  of  the  conclusion  is  called  the 
major  term  on  account  of  its  being  naturally 
more  extensive  than  the  subject.  By  the 
rule  it  is  undistributed  in  affirmative  proposi- 
tions, that  is,  it  has  applications  beyond  the 
subject.     Part  II,  Sec.  iv,  28. 

In  the  example,  deserving  death  is  applicable 
to  many  besides  Cesar. 

7.  Every  regular  syllogism  contains  three, 
and  only  three  propositions,  called  the  Major 
premise,  the  Minor  premise,  and  the  Conclu- 
sion. 

8.  The  Major  Premise  is  that  in  which  the 
major  term  is  compared  with  the  middle  term 

Major  Premise.   All  tyrants  deserve  death; 
Cesar  was  a  tyrant; 
Therefore,  Cesar  deserved  death.    ^ 


60  ELEMENTS  OF  LOGIC. 

9.  The  Minor  Premise  is  that  in  which  the 
minor  term  is  compared  with  the  middle 
term;  as, 

All  tyrants  ('eserve  death ; 
Minor  Premise.  Cesar  was  a  tyrant ; 

Therefore,  Cesar  deserved  death. 

10.  The  Conclusion  is  that  in  which  the 
major  and  the  minor  terms  are  compared  to- 
gether. 

All  tyrants  deserve  death ; 
Cesar  was  a  tyrant ; 
Conchision.    Therefore,  Cesar  deserved  death. 

11.  In  every  regular  syllogism  the  major 
premise  is  placed  first,  the  minor  next,  and  the 
3on elusion  last. 

EXAMPLES. 

1.  All  the  faithful  are  dear  to  God ; 
Some  that  are  afflicted  are  faithful ; 
Therefore,  some  that  are  afflicted  are  dear 

to  God. 

2.  No  work  that  exhibits  marks  of  design 

can  be  the  effect  of  chance ; 
The  world  exhibits  marks  of  design, 
Therefore,  the  world  cannot  be  the  effect 

of  chance. 


THE   RULES  OF  SYLLOGISM.  61 

3.  That  which  improves  the  mind  is  useful ; 
Study  improves  the  mind ; 
Therefore,  study  is  useful. 

4.  No  literary  production  is  perfect. 
This  treatise  is  a  literary  production ; 
Therefore,  this  treatise  is  not  perfect. 

5.  Every  vegetable  is  combustible ; 
Every  tree  is  a  vegetable ; 
Therefore,  every  tree  is  combustible. 

SECTION  II. 

THE   RULES    OF   SYLLOGISM. 

12.  The  validity  of  all  arguments  may  be 
tested  by  the  logical  axiom  (3) ;  and  no  syllo- 
gism is  valid  which  does  not  conform  to  it. 

13.  It  cannot,  however,  always  be  directly 
and  conveniently  applied;  as,  for  example,  in 
the  following  valid  syllogism : 

No  virtues  are  evils ; 

All  virtues  are  difficult ;  therefore, 

Some  difficult  things  are  not  evils. 

Tliis  syllogism  may  be  altered  by  converting 
the  minor  premise,  and  then  it  will  plainly 
appear  to  conform  to  the  logical  axiom;  thus. 


62  ELEMENTS  OF  LOGIC. 

No  virtues  are  evils ; 

Some  diflScult  things  are  virtues ;  therefore, 

Some  difficult  things  are  not  evils. 

14.  But  to  avoid  the  inconvenience  of  alter- 
ing a  syllogism,  in  order  to  apply  the  logical 
axiom,  logicians  have  adopted  the  following 
canons  and  rules  by  which  to  test  the  validity 
of  syllogisms. 

15.  Canon  I.  If  two  terms  agree  with  one 
and  the  sa/me  thirds  they  agree  with  each  other. 

16.  Canon  II.  If  one  term  agrees  and  the 
other  disagrees  with  one  a/nd  the  same  thirds 
these  two  disagree  with  each  other. 

This  agreement  must  be  understood  to  be 
that  kind  of  class  relation  explained  by  the 
logical  axiom,  and  required  by  Aristotle's 
dictum,  otherwise  the  canons  will  mislead. 

Silver  is  a  mineral ; 
Platina  is  a  mineral ; 

Will   not  prove  that  platina  is  silver,  though 
these    terms    agree    with    the    term    mineral. 

All  studies  which  tend  to  increase  national  and  private 
wealth  are  useful; 

The  studies  at  Oxford  do  not  tend  to  increase  national 
and  private  wealth; 

Therefore,  the  studies  at  Oxford  are  not  useful. 


THE  RULES  OF  SYLLOGISM.  63 

This  might  at  first  seem  to  be  founded  on 
canon  II,  but  it  is  a  fallacy,  as  is  easily  seen  in 
a  cafee  precisely  parallel. 

All  cultivated  plants  grow  • 

The  wild  rose-bush  is  not  cultivated; 

Therefore,  the  wild  rose-bush  does  not  grow. 

John  Jones  is  sentenced  to  die ; 

The  first  private  in  the  ranks  is  John  Jones ; 

Therefore,  the  first  private  in  the  ranks  is  sentenced  to  die. 

Here  the  first  canon  is  observed,  but  the 
logical  axiom  is  not  complied  with  unless  you 
consider  proper  names  as  distributed  and  stand- 
ing for  a  class  of  one.  See  Part  II,  Sec.  ii,  11 ; 
and  Sec.  iv,  28.  Strictly  this  is  rather  a  case 
of  identification  than  of  inference. 

To  avoid  error,  we  must  add  to  the  two 
canons  the  following  five  rules  or  cautions: 

RULE  I. 

17.  Every  syllogism  must  have  three^  and 
only  three  terrm^  am,d  three^  ami  only  three^ 
propositions. 

Ambiguous  terms  are  to  be  considered  as 
two  terms. 


64  ELEMENTS  OF  LOGIC. 

The  following  example  has,  in  reality,  foui 
terms : 

Repentance  is  a  good  thing ; 
Wicked  men  abound  in  repentance ; 
Therefore,  wicked  men  abound  in  a  good  thing. 

If  the  word  repentcmce  be  regarded  as  having 
the  same  meaning  in  both  premises,  then  one 
proposition  or  the  other  is  false. 

Ambiguous  terms  are  fruitful  sources  of  error 
in  argument. 

Sometimes  an  argument  will  appear  to 
have  too  many  terms  when  a  little  alteration, 
not  affecting  the  sense,  will  show  but  three; 
thus: 

No  irrational  agent  could  produce  a  work  which  manifests 

design ; 
The  universe  is  a  work  which  manifests  design ; 
Therefore,  no  irrational  agent  could  have  here  produced 

the  universe ; 

This  seems  to  have  five  terms,  but  the  first  pre- 
mise is  properly: 

A  work  that  manifests  design  could  not  be  produced  bj 
an  irrational  agent. 


THE  BULES  OF  SYLLOGISM.  65 

RULE  n. 

18.  The  middle  term  must  he  distributed  once 
at  least  in  the  premises. 
The  following  example  violates  the  rule : 

Granite  is  a  mineral ; 
Lead  is  a  mineral ; 
Therefore,  lead  is  granite. 

The  middle  term  mineral  is  undistributed; 
hence,  granite  is  compared  to  mineral  in  a 
part  of  its  extension,  and  lead  is  compared  to 
it  in  another  part  of  its  extension ;  therefore, 
neither  of  the  canons  of  logic  are  complied 
with,  for  the  two  extremes  are  not  compared 
to  one  and  the  same  third. 

The  following  seems  to  violate  the  rule: 

True  patriots  are  disinterested ; 
Few  men  are  disinterested ; 
Therefore,  few  men  are  true  patriots. 

But  by  putting  the  minor  premise  in  another 
form,  and  transposing  the  premises,  it  would 
stand  thus: 

Disinterested  men  are  ftw ; 

True  patriots  are  disinterested; 

Therefore,  true  patriots  are  few. 
5 


66  ELEMENTS  OF  LOGIC. 

BULE  m. 

19.  No  tenn  must  he  distributed  m  the  con- 
cUision^  which  was  not  disPnbuted  in  one  of  tJu 
premises. 

The  following  violates  the  rule: 

Some  diseases  are  contagious ; 

No  rheumatic  fevers  are  contagious ; 

Therefore,  rheumatic  fevers  are  not  diseases. 

Here  you  employ  the  term  diseases  in  the 
whole  of  its  extent  in  the  conclusion,  while  you 
employ  it  in  only  a  part  of  its  extent  in  the 
premise. 

RULE  IV. 

20.  Two  negaime  or  two  jpartiaula/r  premises 
prove  nothing.     As, 

Slate  is  not  a  metal. 
Mint  is  not  a  metal. 

Here  two  terms  disagree  with  a  third.  This 
is  not  according  to  the  canons,  which  requires 
either  that  both  should  agree  with  the  third,  or 
one  agree  and  the  other  disagree. 

Some  bad  men  are  eloquent  orators ; 
Some  good  men  are  eloquent  orators ; 
Therefore,  some  good  men  are  bad  men. 


THE  RULES  OF  SYLLOGISM.  67 

Here  you  have  the  middle  term  undis- 
tributed, which  is  contrary  to  Rule  2,  and 
therefore,  not  according  to  the  canons. 

Some  bad  men  are  eloquent  orators ; 
Some  good  men  are  not  eloquent  orators ; 
Therefore,  some  good  men  are  not  bad  men. 

This  is  contrary  to  Eule  3. 

The  following  syllogism  with  negative 
premises  may  be  made  regular  by  considering 
one  of  them  an  affirmative: 

No  man  is  happy  who  is  not  secure ; 
Ko  tyrant  is  secure ; 
Therefore,  no  tyrant  is  happy. 

No  man  who  is  insecure  is  happy ; 
Every  tyrant  is  insecure; 
Therefore,  no  tyrant  is  happy. 

RULE  V. 

21.  If  either  premise  he  negative  or  particu- 
lar, so  also  is  the  conclusion.    As, 

No  virtuous  man  is  a  rebel ; 
X  and  Y  are  virtuous  men ; 
Therefore,  X  and  Y  are  not  rebels. 


^8  BLEMENTS  OP  LOGIC. 

Here  one  term  '5  said  to  disagree  >^ith  a 
middle  and  the  other  to  agree,  hence  thej  dis- 
agree with  each  other,  and  the  conclusion 
must  be  negative. 

All  who  study  diligently  deserve  reward ; 
Some  scholars  study  diligently ; 
Therefore,  some  scholars  deserve  reward. 

Here  is  a  particular  premise,  and  you  cannot 
draw  anything  but  a  particular  conclusion,  for 
a  universal  conclusion  Would  be  contrary  to 
Rule  3,  and  against  the  canons. 

The  following  in  form  violates  the  first  part 
of  this  rule,  but  it  might  be  stated  so  as  to  be 
regular. 

None  but  candid  men  are  good  reasoners. 

Few  infidels  are  candid ; 

Therefore,  few  infidels  are  good  reasoners. 

It  may  be  changed  thus : 

All  good  reasoners  are  candid; 

Most  infidels  are  not  candid ; 

Therefore,  most  infidels  are  not  good  reasoners. 

Or  thus : 

Those  wh6  are  uncandid  are  not  good  reasoners; 

Most  infidels  are  uncandid; 

Therefore,  most  infidels  are  not  good  reasoners. 


THE  RULES  OP  SYLLOGISM.  69 

EXAMPLES. 

L.  Ko  one  is  free  who  is  enslaved  by  his  ap- 
petites ; 
A  sensualist  is  enslaved  by  his  appetites ; 
Therefore,  a  sensualist  is  not  free. 

2.  All  gold  is  precious ; 
This  mineral  is  precious; 
Therefore,  this  mineral  is  gold. 

3.  All  wise  legislators  adapt  their  laws  to  the 

genius  of  the  people ; 
Solon  adapted  his  laws  to  the  genius  of  the 

people ; 
Tlierefore,  Solon  was  a  wise  legislator. 

4.  All  pious  men  desire  the  freedom  of  their 

country ; 
Thomas  Paine  desired  the  freedom  of  his 

country ; 
Therefore,  Thomas  Paine  was  a  pious  man. 

5.  Warm  countries  alone  produce  wine; 
Spain  is  a  warm  country ; 
Therefore,  Spain  produces  wine. 

6.  Some  poisons  are  vegetables ; 
No  poisons  are  useful  drugs ; 
Therefore,  some  useful  drugs  are  not  vege 

tables. 


70  ELEMENTS  OF  LOGIC. 

7.  They  who  subvert  the  foundations  of  mo- 

rality ought  not  to  be  respected ; 

Atheists  subvert  the  foundations  of  mo- 
rality ; 

Therefore,  Atheists  ought  not  to  be  re- 
spected. 

8.  All  vegetables  grow; 
This  animal  grows; 

Therefore,  this  animal  is  a  vegetable. 

9.  Most  men  are  poor ; 
Most  men  are  intelligent ; 

Therefore,  some  intelligent  men  are  poor. 

10.  Light  is  contrary  to  darkness  ; 
Feathers  are  light ; 

Therefore,  feathers  are  contrary  to  dark- 
ness. 

11.  An  enslaved  people  is  not  happy ; 

The  English  are  not  an  enslaved  people ; 
Therefore,  the  English  are  happy. 

12.  None  but  whites  are  civilized; 

The  Ancient  Germans  were  whites ; 
Therefore,  they  were  civilized. 

13.  None  but  whites  are  civilized ; 
The  Hindoos  are  not  whites ; 
Therefore,  they  are  not  civilized. 


IRREGULAR  SYLLOGISMS.  71 

14.  None  but  civilized  people  are  white; 
The  Gauls  were  white; 
Therefore,  the  Gauls  were  civilized. 

SECTION    III. 

IRREGULAR   SYLLOGISMS. 

22.   The  Enthymeme  is  a  defective  syllo^ 
ism,  having  one  premise  suppressed;  as, 

Christianity  teaches  the  way  to  future  happiness ; 
Therefore,  it  should  be  diligently  sought. 

Here  the  major  premise  is  suppressed.     Sup- 
ply it,  and  the  syllogism  is  complete ;  thus. 

Whatever  teaches  the  way  to  future  happiness  should 
be  diligently  sought ; 
Christianity  teaches  the  way  to  future  happiness ; 
Therefore,  Christianity  should  be  diligently  sought. 

Every  man  is  mortal ; 
Therefore,  every  king  is  mortal. 

Here  the  minor  premise  is  omitted.  (9.) 
Frequently  the    conclusion  •is   stated   first ; 
thus. 

Enthusiasm  should  be  avoided. 
Because  it  leads  astray  from  reason. 


72  ELEMENTS  OF  LOGIC. 

23.  A  regular  syllogism  may  be  changed 
into  an  Enthymeme  by  simply  suppressing  one 
of  the  premises,  or  by  stating  the  conclusion 
first,  and  joining  thereto  one  of  the  premises  by 
the  conjunction  for^  aSy  or  hecause.    As, 

Whatever  enables  us  to  overcome  difficulties  is  nseM ; 
Perseverance  enables  us  to  overcome  difficulties; 
Therefore,  perseverance  is  useftd. 

This  may  be  changed  to  Enthymeme,  thus : 

Whatever  enables  us  to  overcome  difficulties  is  useful ; 
Therefore,  perseverance  is  usefuL 

Or  thus : 

Perseverance  enables  us  to  overcome  difficulties; 
Therefore,  perseverance  is  usefuL 

Or  thus : 

Perseverance  is  useful,  for  it  enables  us  to  overcome 
difficulties. 

Or  thus : 

Perseverance  is  useful ;  for, 

Whatever  enables  us  to  overcome  difficulties  is  useful 

24.  To  reduce  an  Enthymeme  to  a  syllogism, 
observe  first  what  is  the  conclusion  or  point 


TRREGULAB  SYLLOGISMS.  78 

established.  This  contains  the  minor  and  major 
terms,  (10)  and  the  remaining  term  must  be  the 
middle  term.  Having  these,  the  syllogism  maj 
be  easily  constructed  according  to  the  rules 
(Sec.  I.)  by  supplying  the  implied  premise. 

In  the  last  example,  persevera/nce  is  useful^  is 
the  conclusion.  Consequently  the  remaining 
term,  enables  us  to  wercome  difficulties^  is  the 
middle  term.  (6.)  Persemrcmce  enables  us  to 
overcome  difficulties  is  implied,  and  makes  the 
minor  premise.  (9.) 

25.  The  Sorites  is  a  continued  argument, 
consisting  of  a  series  of  propositions  arranged 
in  such  a  manner  that  the  predicate  of  each 
forms  the  subject  of  the  following  proposition, 
except  the  concluding,  which  takes  the  subject 
of  the  first  proposition ;  as. 

There  can  be  no  enjoymeni  of  property  withoTit  gov- 
ernment ; 

No  government  without  laws  enforced; 

No  laws  enforced  without  a  magistrate ; 

No  magistrate  without  obedience ; 

And  no  obedience  where  every  one  acts  as  he  pleases ; 
therefore, 

There  can  be  no  enjoyment  of  property  where  every 
)ne  acts  as  he  pleases. 


74  ELEMENTS  OF  LOGIC. 

26.  Every  Sorites  contains  as  many  syllo- 
gisms as  there  are  propositions  intervening 
between  the  first  and  the  last  proposition. 

The  English  are  a  brave  people; 
A  brave  people  are  free ; 
A  free  people  are  happy ; 
Therefore,  the  EngUsh  are  happy. 

This  may  be  broken  up  into  two  syllogisms,  thus 

« 
A  brave  people  are  free ; 
The  English  are  a  brave  people ; 
Therefore,  the  English  are  free. 

A  free  people  are  happy ; 
The  English  are  a  free  people ; 
Therefore,  the  English  are  happy. 

27.  The  Epiohieema  is  a  compound  argu- 
ment, of  which  one  or  both  the  premises  are 
separately  proved  before  the  conclusion  is 
drawn.     As, 

Unjust  laws  endanger  the  stability  of  government,  f(n 
they  create  discontent  among  the  people; 

Laws  restraining  freedom  of  conscience  are  unjnst,  fo7 
they  require  the  people  to  abandon  their  dea/reat  c&neems; 

Therefore,  laws  restraining  freedom  of  conscience  en- 
danger the  stability  of  government. 


IRREGULAR  SYLLOGISMS.  76 

28.  Irregular  syllogisms  are  the  most  com- 
oionly  employed  in  discourses  of  every  kind : 
for  the  regular  form  of  syllogism  would  not 
often  consist  with  elegance  of  style,  nor  is  it 
often  requisite  to  produce  conviction. 

EXAMPLES. 

1.  The  mind  is  a  thinking  substance ; 
A  thinking  substance  is  a  spirit ; 

A  spirit  has  no  composition  of  parts ; 
That  which  has  no  composition  of  parts 

is  indissoluble ; 
That  which  is  indissoluble  is  immortal ; 
Therefore,  the  mind  is  immortal. 

2.  He  is  a  good  man,  therefore  he  is  happy. 

3.  He   is  a   miserable  man,   because  he  is 
''  vicious. 

4.  Whatever  tends   to   subvert   government 

should  be  deprecated ; 
Therefore,  civil  dissensions  should  be  dep- 
recated. 

5.  Every  man  is  an  animal ; 

Every  animal  is  a  living  creature ; 
Every  living  creature  is  a  substance ; 
Therefore,  every  man  is  a  substance. 


76  ELEMENTS  OF  LOGIC. 

6.  A  religion  attested  by  miracles  is  from  God, 

for  none  but  God  can  suspend  the  laws 
of  nature,  and  God  would  not  permit 
them  to  be  suspended  but  for  his  glory. 

The  Christian  religion  was  attested  by 
miracles,  for  the  friends  and  the  enemies 
of  Christianity  have  agreed  in  declaring 
it  was; 

Therefore,  the  Christian  religion  is  from 
God. 

7.  No  opinion  that  tends  to  immorality  should 

be  embraced. 
Atheistical    sentiments    tend     to    immo- 
rality ; 
Therefore,   atheistical  sentiments  should 
not  be  embraced. 

8.  It  is  lawful  for  one  man  to  kill  anothei* 

who  lies  in  wait  to  kill  him,  for  the  laws 

of  nature  and  the  customs  of  mankind 

sanction  it ; 
Clodius  lay  in  wait  to  kill  Milo,  for  his 

equipage,    arms,    guards,    movements, 

etc.,  prove  it ; 
Therefore,  it  was  lawful  for  Milo  to  kill 

Clodius. 


HYPOTHETICAL  SYLLOaiSMS.  77 

9.  With  some  of  them  God  was  not  well 
pleased,  for  they  were  overthrown  in  the 
wilderness. 

10.  He  that  is  of  God  heareth   my  words; 

ye  therefore  hear  them  not,  because  yo 
are  not  of  God. 

11.  Men  are  free  agents,  for  they  are  account- 

able beings. 

12.  Skepticism  is  an  enemy  to  man,  since  it  is 

an  enemy  to  truth. 

• 

SECTION  lY. 

HYPOTHETICAL  SYLLOGISMS DILEMMA. 

Hypothetical  Syllogisms  are  of  tWo  kinds: 
Conditional  and  Disjunctive. 

29.  A  Conditional  Syllogism  is  one  in  which 
the  major  premise  is  a  conditional  proposition ; 
as. 

If  there  is  a  God,  this  world  is  governed  by  a  provi 
dence; 
Bik  there  is  a  God ; 
Therefore,  this  world  is  governed  by  a  providence. 

30.  The  clause  containing  the  condition  is 
called  the  Antecedent,  that  containing  the  as- 
sertion is  called  the  Consequent. 


78  ELEME-NTS  OP  LOGIC. 

81.  Rule.  If  the  cmtecedent  he  granted  so  is 

the  consequent^  if  the  consequent  le  denied  so  is 

• 

the  antecedent  I  hut  not  vice  versa;  that  is,  the 
antecedent  heing  denied  proves  nothing^  cmd  the 
consequent  hemg  granted,  proves  nothing  j  as, 

If  Samuel  is  a  father  he  has  authority; 
But  Samuel  is  a  father ; 
Therefore,  he  has  authority. 

If  Samuel  is  a  father  he  has  authority ; 
But  he  has  not  authority ; 
Therefore  he  is  not  a  father. 

But  vice  versa,  the  argument  is  not  valid. 

If  Samuel  is  a  father  he  has  authority ; 
Bbt  Samuel  is  not  a  father ; 
Therefore,  he  has  not  authority. 

But  lie  might  have  authority  from  some  other 
relation  or  office.     Again, 

If  Samuel  is  a  father  he  has  authority ; 
But  he  has  authority ; 
Therefore,  he  is  a  father. 

32.  Conditional  Syllogisms  may  be  reduced  to 
regular  syllogisms,  by  considering  the  anteced- 
ent tbe  subject,  and  the  consequent  the  pr<».dicate 
of  an  universal  affirmative  propositio 


HYPOTHETICAL  SYLLOGISMS.  79 

If  the  Atheists  are  right  the  world  exists  withoQt  a 
oause ; 
But  the  Atheists  are  not  right ; 
Therefore,  the  world  does  not  exist  without  a  cause. 

Reduced  thus,  when  it  appears  a  fallacy  : 

The  case  of  the  Atheists  being  right  is  the  case  of  the 
world  existing  without  a  cause ; 

But  the  present  case  is  not  the  case  of  the  Atheist  being 
right; 

Therefore,  the  present  case  is  not  the  case  of  the  world 
existing  without  a  cause.   (See  Rule  3,  Sec.  ii.) 

33.  A  DisJUNcrrivE  Syllogism  is  one  whose 
major  premise  is  a  disjunctive  proposition. 

The  earth  either  moves  in  a  circle  or  an  ellipse. 
But  the  earth  does  not  move  in  a  circle ; 
Therefore,  it  moves  in  an  ellipse. 

It  is  either  spring,  summer,  autumn,  oi  winter' 
But  it  is  not  summer,  autumn,  or  winter ; 
Therefore,  it  is  spring. 

34.  Disjunctive  syllogisms  are  easily  con- 
vertible into  conditional,  and  so  brought  under 
the  foregoing  rules ;  as, 


80  ELEMENTS  OP   LOGIC. 

if  the  earth  does  not  move  hi  a  ch*cle  it  moves  in  an 
ellipse ; 
But  it  does  not  move  in  a  circle ; 
Therefore,  it  moves  in  an  ellipse. 

35.  The  Dilemma  is  a  complex  conditional 
syllogism,  of  which  the  major  premise  contains 
two  or  more  conditional  propositions,  and  the 
minor  a  disjunctive  proposition ;  as, 

If  A  is  B,  0  is  D,  and  if  E  is  F,  G  is  H; 
But  either  A  is  B  or  E  is  F ; 
Therefore,  0  is  D  or  G  is  H. 

If  ^schines  joined  in  the  public  rejoicings  he  is  iucon- 
sistent ;  if  he  did  not  he  is  unpatriotic ; 

But  ^schines  either  did  or  did  not  join  in  the  public 
rejoicings ; 

Therefore,  he  is  either  inconsistent  or  unpatriotic. 

The  advantage  of  the  Dilemma  is  this :  that 
you  may  not  be  able  to  affirm  or  deny  any 
proposition,  but  you  may  always  state  it  dis- 
junctively. Demosthenes  might  not  be  able  to 
prove  that  .^chines  did  join  in  the  public  re- 
joicing, or  that  he  did  not  join ;  but  certainly 
he  did  or  he  did  not. 

This  Dilemma  may  easily  be  reduced  to  two 


OF 

DILEMMA.  81 

or  more  conditional  syllogisms  and  these  to 
regular  syllogisms. 

36.  Thus  all  hypothetical  syllogisms  as  weU 
as  all  otlier  arguments  may  be  reduced  to  regu- 
lar syllogisms,  and  so  subjected  to  the  test  of 
the  logical  axiom.  But  it  is  more  convenient 
in  ordinary  practice  to  try  them  by  their  own 
rules. 

EXAMPLES. 

1.  If  this  man  has  a  fever,  he  is  sick ;  ^S^ 
But  he  is  sick ; 

Therefore,  he  has  a  fever. 

2.  The  world  was  created  by  chance,  or  by 

an  intelligent  agent ; 
But  it  was  not  created  by  chance ; 
Therefore,  it  was  created  by  an   intelli 

gent  agent. 

3.  If  Louis  Phihppe  is  a  good  king  France  is 

likely  to  prosper ; 
But  Louis  Philippe  is  a  good  king  ; 
Therefore,  France  is  likely  to  prosper. 

4:.  If  C  be  not  the  center  of  the  circle  some 

other  point  must  be ; 

But  no  other  point  can  be  the  center ; 

Therefore,  C  is  the  center  of  the  circle. 
6 


82  ELEMENTS   OF  LOGIC. 

6.  If  this  man  were  wise  he  would  not  speak 
irreverently  of  the  Scriptures  in  jest; 
if  he  were  good,  he  would  not  do  so  in 
earnest ; 
But  he  does  it  either  in  jest  or  in  earnest ; 
Therefore,  he  is  either  not  wise  or  he  is 
not  good. 

6.  If  logic  is  useless  it  deserves  to  be  neg 

lected ; 

But  logic  is  not  useless ; 

Therefore,  it  does  not  deserve  to  be  neg- 
lected. 

7.  Either  money  or  produce  will  be  scarce 

in  the  market; 
But  produce  will  not  be  scarce ; 
Therefore,  money  will  be  scarce. 

8.  If  W.  were  a   general   he   would    have 

power ; 
But  W.  is  not  a  general ; 
Therefore,  he  has  not  powei. 

9.  If  W.  be  a  general  he  must  be  obeyed ; 
But  W.  must  be  obeyed ; 
Therefore,  he  is  a  geueraL 


DISTINCTIONS  OF   REASONING.  83 

SECTION  Y. 

DISTINOTIONS    OF   KEASONING. 

1.  The  divisions  of  reasoning  into  Deduction 
and  Induction,  Mathematical  and  Moral,  De- 
monstrative and  Probable,  by  Analogy,  A 
priori,  A  posteriori,  A  fortiori,  Reductio  ad  ab- 
surdum,  and  Reductio  ad  impossibile,  are  only 
different  ways  of  laying  down  premises,  the 
process  of  reasoning  being  always  the  same, 
namely,  deductive — from  generals  to  particulars. 

The  degree  of  certainty  in  the  conclusion, 
when  the  process  of  inference  is  correct, 
depends  upon  the  degree  of  certainty  in  the 
premises. 

2.  In  Pure  Mathematical  REAsoiaww,  the 
principles  and  judgments  beipg  always  self-evi- 
dent, the  conclusions  are  absolutely  certain ;  in 
Mixed  Mathematics  self-evident  axioms  and 
judgments  are  mixed  with  matters  of  fact 
and  measurements  of  instruments,  to  which 
some  uncertainty  is  attached;  consequently 
the  same  uncertainty  attaches  to  the  conclu- 
sion. 


84  ELEMENTS  OF  LOGIC. 


EXAMPLE. 

If  a  straight  line  meet  another  straight  U7ie^ 
the  sum  of  the  adjacent  angles  will  he  equal  to 
two  right  amgles. 

Suppose  the  straight  line  DC  E       p 

meets    the    straight   line  A  B 
at  the  point  C;   then  will  the 
angles  A  0  D  and  D  C  B  to-  ^        0       B 
gether  be  equal  to  the  two  right  angles  ACE 
and  E  C  B. 


Axiom. — A  whole  is  equal  to  the  sum  of  all  its  parts. 

A  0  D  is  a  whole  of  which  A  0  E  and  E  0  D  are  its 
parts. 

Therefore,  A  0  D  is  equal  to  all  its  parts,  namely, 
A  0  E  and  E  0  D. 

Axiom. — If  equals  be  added  to  equals  the  sum  is  equal ; 
BOB  added  to  ^  0  D,  and  D  0  B  added  to  A  0  E 
plus  E  0  D  are  equals  added  to  equals. 
Therefore,  the  sum  is  equal. 

Now,  as  A  C  E  is  one  of  the  right  angles  in 
question,  you  have  only  to  prove  that  the  other 
two  angles  E  C  D  and  D  C  B  equal  the  othei 
right  angle  E  C  B. 


DISTINCTIONS  OF  REASONING.  85 

The  sum  of  all  the  parts  is  equal  to  the  whole. 

E  0  D  plus  D  0  B  are  all  the  parts  of  the  angle  E  0  B 

Therefore,  they  are  equal  to  the  whole  E  0  B. 

Thus  you  have  proved  that  DOB  added  to 
A  C  D  is  equal  to  A  C  E  added  to  E  C  B. 

This  is  a  case  of  pure  mathematics,  because  I 
have  supposed  D  C  a  straight  line  meeting 
another  A  B ;  but  if  I  take  a  rod  and  make  a 
line  between  two  points  on  a  field,  I  do  not  know 
that  it  is  in  reality  a  perfectly  straight  line. 
Hence,  there  is  a  mixture  of  practical  uncer- 
tainty, with  the  absolute  certainty  of  the 
axioms  employed  in  any  ^calculation  about  it ; 
hence,  such  calculation  is  called  mixed  mathe- 
matics. 

3.  Induction  is  a  course  of  argument  by 
which,  from  the  principles  of  causation,  joined 
with  particular  phenomena,  we  infer  the  gen- 
eral law  of  those  phenomena. 

Some  of  the  principles  of  causality  are  the  fol- 
lowing :  No  events  no  phenorrienon  happens 
t'nthout  a  cause.  Like  material  causes  jproduce 
like  effects.  No  cause  can  operate  where  it  is 
not. 

From  the  principles  we  directly  infer  the  pos- 
tulate :  The  immediate  and  invariable  contecedent 


86  fiLEME^TTS  OF  LOGIC. 

of  any  ^phenomenon  may  he  presumed  to  he  its 
cause  or  contain  its  cause. 

Jn  respect  to  spiritual  agencies  tlie  principles 
of  causation  are  the  same,  except  in  relation  to 
the  will,  whose  distinguishing  characteristic  is 
freedom.  Of  this  alone  we  cannot  predicate 
that  like  causes  will  produce  like  eflPects.  We 
cannot  certainly  know  how  it  will  behave  under 
any  circumstances. 

It  should  be  observed,  that  it  may  be  beyond 
human  power  to  perceive,  w^hen  any  physical 
change  takes  place,  what  the  real  cause  is; 
but  we  know  that  it  must  be  found  where  the 
event  takes  place,  and  that  the  invariable  and 
immediate  antecedent  of  the  event  must  con- 
tain it. 

To  discover  the  cause,  therefore,  of  any  phe- 
nomenon, we  must  observe  under  what  circum- 
stances that  phenomenon  happens  and  notice  its 
invariable  antecedent. 

Having  done  this  we  are  prepared  to  make 
the  proper  inference,  and  the  whole  process  ca# 
be  put  into  a  syllogism  with  the  particular 
cause,  as  discovered  in  one  or  two  cases,  for  a 
minor  premise,  and  a  principle  of  causation  for 
a  major  premise.     The  principles  of  causality 


DISTINCTIONS  OF   REASONING.  87 

are  intuitively  true,  like  the  axioms  of  mathe- 
matics ;  hence,  induction  has  the  same  certainty 
as  mixed  mathematics. 

EXAMPLE. 

The  law  of  magnetic  attraction,  or  that  the 
magnet  will  always  attract  iron,  is  proved  thus : 

A  material  cause  will  always  produce  the  same  effect. 

Or,  more  particularly, 

"Whatever  is  the  cause  of  the  attracting  of  iron  in  one 
or  two  cases  will  always  attract  iron ; 
A  magnet  is  the  cause  of  attracting  iron  in  one  or  twc 


Therefore,  it  will  always  attract  iron. 

ITow  how  do  we  know  that  it  was  the 
magnet  and  not  something  else  that  caused  the 
iron  to  move  ? 

We  must  make  several  experiments,  and 
apply  the  following  rule : 

BITLE   FOR   OBSERVATION. 

If  a  phenomenon  he  preceded  hy  anything^  so 
that  when  that  thing  is  present  in  different  dr- 
efimsta/nces  that  phenomenon  takes  place,  but 


88  ELEMENTS  OF   LOGIC. 

does  not  take  jplace  when  that  thing  is  absent 
though  the  circumstances  remain  the  saine^  tJien 
that  thing  is  the  cause  of  the  ^phenomenon  or 
contains  the  cause, 

.  This  rule  will  show,  on  making  a  few  experi 
ments,  that  the  magnet  is  the  cause  of  the  at- 
traction of  iron. 

Some  things  will  not  admit  of  the  latter  part 
of  the  rule  being  applied,  as  matter,  gravita- 
tion, electricity,  etc.,  can  never  be  absent  from 
any  event  in  this  world. 

This  rule  in  its  two  parts  may  be  symbolically 
exhibited  thus: 

Part  I.— A  BO.        A  D  E. 
a  b  c.         a  d  e. 

Let  a  represent  a  phenomenon,  and  A  some- 
thing supposed  to  be  its  cause.  In  one  case  A 
has  the  circumstances  or  adjuncts  B  C,  in  the 
other  case  different  circumstances,  D  E.  Now 
a  appearing  with  A  in  different  circumstances 
shows  the  latter  to  be  its  cause. 

Part  II.—N0W,  if  we  have  ABO.      B  Q 

a  b  c.  be, 
this  will  show  the  absence  of  a  when  A  is 
absent,  though  the  circumstances  which  at- 
tended A  remain  the  same. 


DISTINCTIONS  OF    REASONING.  89 

Sometimes  the  particular  cause  is  obtained  "by 
testimony  or  revelation,  and  you  have  only  to 
supply  the  major  premise.  Thus,  we  know  God 
predicted  contingent  events  in  the  prediction 
concerning  the  sins  of  Judas  and  Peter,  and 
from  this  we  prove  his  absolute  foreknowledge. 

In  this  case  the  arguments  would  stand  thus ; 

Whoever  can  predict  contingent  events  foreknows  aU 
things. 
God  has  predicted  contingent  events ; 
Therefore,  God  foreknows  all  things. 

To  prove  the  minor  premise  we  may  say — 

Human  transgressions  are  contingeut  events ; 
God  has  predicted  human  transgressions  in  the  case  of 
Judas  and  Peter ; 
Therefore,  God  has  predicted  contingent  events. 

By  induction  the  psychologist  discovers  dis- 
tinctions between  the  powers  of  the  mind ;  for 
example,  that  sensation  and  perception  cannot 
give  the  idea  of  space,  but  some  other  power 
called  intuition  or  the  reason. 

4.  Reasoning  from  Analogy  is  arguing  with 
premises  made  up  of  principles  and  judgments 
respecting  similar  things,  or  things  that  are  alike 
in  some  relations.  This  definition  would  in- 
clude induction,  as  treated  by  most  writers  on 


90  EliEMENTS  OP  LOGIC. 

the  subject;  but  I  consider  the  difference  to 
be  very  important,  because  the  principles  on 
which  Induction  is  based  -are  certainties,  but 
"■hose  of  Analogy  are  but  probabilities. 

Some  of  the  principles  on  which  reasoning  by 
Analogy  is  based  are  : 

Sirrdla/r  causes  will  "be  likely  to  ^produce  simir 
la/r  effects. 

Things  that  resemble  each  other  in  certain  at- 
i/Hhutes  or  relat/ix)ns  will  he  likely  also  to  resem- 
hU  each  other  in  some  other  attributes  or  relations. 

An  att/rihute  found  in  several  individuals  be- 
longs to  their  class.  [This  is  the  old  principle  of 
/nduction.] 

Thus,  horned  animals  have  cloven  hoofs,  is  a 
law  in  natural  history,  and  is  proved  thus : 

Animals  that  resemble  each  other  in  some  attributes  are 
likely  to  resemble  each  other  in  other  attributes ; 

All  horned  animals  resemble  the  ox,  sheep,  etc.,  in  being 
horned ; 

Therefore,  they  will  be  likely  to  resemtle  them  in  other 
attributes  as  having  cloven  hoofs. 

In  the  following  example  the  conclusion  dis- 
agrees with  facts : 

An  attribute  of  a,  b,  and  c  clovers  is  likely  to  belong  to 


DISTINCTIONS  OF    REASONING.  91 

5.  Keasoning  a  Priori  is  reasoning  from 
antecedents  to  consequents.  Thns,  the  idea 
of  God,  the  perfect  and  infinite  One,  is  proved 
true  by  the  pre-existing  ideas  of  infinity  and 
perfection. 

Every  necessary  and  universal  idea  of  the  human  mind 
must  indicate  a  reality; 

The  ideas  of  the  perfect  and  infinite  are  necessary  and 
universal  in  the  human  mind ; 

Therefore,  they  indicate  a  reality. 

6.  Eeasoning  a  Posteriori  is  reasoning  from 
consequents  to  antecedents. 

Whatever  exhibits  marks  of  design  proves  an  intelligent 
author ; 
The  world  exhibits  marks  of  design ; 
Therefore,  the  world  proves  an  intelligent  author. 

7.  Eeasoning  a  Fortiori  is  inferring  a  judg- 
ment from  premises  which  have  already  been 
admitted  to  prove  a  point  less  probable. 

If  robbery  deserves  imprisonment,  much  more  doea 
highway  robbery. 

If  God  foresees  contingent  events  he  must  foresee  neces- 
sary events. 


92  ELEMENTS  OF    LOGIC. 

8.  Reduotio  ad  absurdum  is  proving  that  a 
certain  proposition  is  true,  because  its  contra- 
diction involves  an  absurdity. 

9.  Reductio  ad  impossibile  is  proving  a  pro 
position  to  be  true  by  showing  that  its  contra 
diction  is  inadmissible. 

These  are  often  employed  in  mathematics. 

10.  Probable  reasoning  is  drawing  infer- 
ences from  premises  that  are  not  certain,  but 
more  or  less  probable. 

When  both  premises  are  of  this  character 
then  the  result  is  not  so  probable  as  either  pre- 
mise, but  as  a  fraction  of  one  of  them. 

Thus,  if  the  probability  of  the  arrival  of  ocean 
mail  to-day  may  be  represented  by  |,  and  the 
probability  of  your  receiving  letters  by  it  is  J, 
then  the  probability  of  your  receiving  letters 
to-day  is  but  J  of  |,  that  is,  }. 

The  rule  is  to  represent  the  jprobability  of 
each  premise  as  compared  with  certainty  hy  a 
fraction^  and  multiply  these  fractions  together 
for  a  result, 

EXAMPLES, 

1.  Thirty-two  degrees  Farenheit  will  always 
freeze  water. 


DISTINCTIONS  OF  REASONING.  98 

2.  Swans  are  white. 

3.  Jupiter  is  inhabited. 

4    If  one  straight  line  cross  another  straight 
line  the  opposite  angles  are  equal. 

5.  The  freedom  of  the  will  is  proved  by  the 

idea  of  liberty. 

6.  The  shadow  of  the  earth  upon  the  moon 

proves  that  it  is  round. 

7.  If  highway  robbery  and  murder  deserve 

death,  piracy  deserves  death. 

8.  A  certain  reporter  is  generally  correct, 

say  five  times  out  of  six.  A  certain 
statement  is  probably  his  report,  the 
probability  being  represented  by  two 
fifths,  what  is  the  probability  of  the 
report  being  true  ? 

9.  If  the  probability  of  your  winning  a  game 

be  one  half,  what  is  the  probability 
of  your  winning  three  games  in  suc- 
cession ? 

10.  The  law  of  terrestrial  gravitation  is  proved 

by  an  apple  falling  to  the  ground. 

11.  A  certain  degree  of  attention  is  necessary 

to  memory,  as  experience  demonstrates. 

12.  Swine   have  horns,  if  what  is  true  of 

individuals  is  true  of  a  class. 


94  ELEMENTS  OF  LOGIC. 

18.   This  servant  will  always  return  in  due 
season,  because  he  always  has  done  so. 

14.  The  emperor  will  declare  war,  becausei 

he  never  submits  to  a  national  insult. 

15.  The  will  is  free,  and  therefore  its  future 

acts  are  unknown  by  even  an  infinite 
mind. 

16.  Ketribution  may  be  expected  in  a  future 

state,  judging  from  the  effects  of  virtue 
and  vice  in  this  life. 

17.  The  will  never  acts  without  some  motive, 

and  therefore,  if  you  know  a  man's 
motives  in  any  case,  you  may  know 
how  he  will  choose. 

18.  This  case  is  typhus  fever,  for  it  exhibits 

many  symptoms  of  that  disease. 

19.  Mercury,    Yenus,    and    the    Earth    are 

opaque,  and  therefore  all  the  planets 
are  opaque. 

20.  The  bull-dog,  terrier,  mastiff,  etc.,  bark, 

tlierefore,  all  dogs  bark. 

21.  Quadrupeds,   birds,   fishes,  etc.,   have  a 

nervous  system ;  therefore,  all  animals 
have  a  nervous  system. 


PART  IV. 


OF   FALLACIES. 

1.  The  fourth  part  of  Logic  treats  of  Falla- 
cies. 

2.  A  Fallacy  is  an  unsound  argument  of 
any  kind. 

3.  Fallacies  are  of  two  kinds;  logical  falla- 
cies and  material  fallacies. 

4.  I.  Logical  Fallacies  are  those  which  in 
form  violate  any  of  the  rules  of  syllogism. 

In  these  the  error  is  entirely  in  the  process 
of  reasoning,  and  the  conclusion  does  not  follow 
from  the  premises ;  as, 

Every  rational  agent  is  accountable; 
Brutes  are  not  rational  agents ; 
Therefore,  brutes  are  not  accountable. 

This  violates  the  third  rule  of  syllogism. 

5.  II.  Material  Fallacies  are  those  which 
in  form  do  not  violate  any  of  the  rules  of  syl 


96  ELEMENTS  OF  LOGIC. 

logism,  but  the  premises  either  are  not  wholly 
true  in  fact,  are  unduly  assumed,  or  result  in  a 
conclusion  not  relevant  to  the  question  which  is 
argued. 

In  material  fallacies  the  fault  is  entirely  in 
the  matter  of  the  propositions,  and  not  in  their 
form  or  connection. 

All  bodies  move  toward  the  center  of  the  universe ; 
All  bodies  move  toward  the  center  of  the  earth ; 
Therefore,  the  center  of  the  earth  is  the  center  of  the 
universe. 

In  this  example  there  is  no  fault  in  the  pro- 
cess of  reasoning;  the  conclusion  results  from 
the  premises,  but  the  minor  premise  contains  a 
statement  which  is  not  true  in  fact. 


Some  logicians  make  a  third  division  of 
fallacies  into  semi-logical,  including  those  made 
by  ambiguous  terms:  for  if  these  terms  aroused 
in  two  senses  they  make  a  logical  fallacy ;  and  if 
they  are  used  in  only  one  sense  they  make  a 
material  fallacy ;  and  you  cannot  always  tell 
which.     A  simple  instance  is  the  following : 

Light  is  contrary  to  darkness ; 

Feathers  are  light ; 

Therefore,  feathers  are  contrary  to  darkness. 


OF    FALLACIES.  97 

6.  Fallacies  are  rarely  presented  in  the  syl- 
logistic form.  They  are  usually  found  in  enthy- 
memes,  and  the  error  lurks  in  the  suppressed 
proposition. 

Sometimes  they  are  offered  in  the  form  of 
questions  so  stated  that  a  false  conclusion  will 
be  likely  to  be  implied. 

7.  Whately  remarks,  All  jests  are  fallacies. 
They  tend  to  excite  laughter  by  betraying  theii 
fallacious  character  while  putting  on  the  air  of 
serious  argument.  The  contrast  amuses.  For 
example :  A  gentleman  seeing  a  young  man 
whom  he  knew  going  by  with  a  looking-glass, 
cried  out,  "Ah,  Joseph,  don't  carry  that  glass 
about,  it  will  reflect  on  you."  This,  reduced  to 
a  syllogism,  will  be  found  to  violate  the  first  rule 
of  syllogism,  by  having  an  equivocal  middle. 

8.  To  determine  whether  an  argument  be 
valid  or  fallacious,  let  the  following  directions 
be  followed. 

EULE. 

Reduce  the  argument  to  a  syllogistic  form.. 
If  it  he  found  incapable  of  taking  that  form 
it  is  of  course  a  fallacy.  If  it  he  reducible  to  a 
njllogism^  ohserve  carefully  the  import  and  the 
number  of  its  terms  am.d  'prepositions^  and  apply 


98  ELEMENTS  OP   LOmC. 

the  rules  of  syllogisms.  If  it  violates  any  of 
them  it  is  a  logical  fallacy.  If  not.,  observe  if 
either  of  the  Remises  he  untrue  or  inadmissible^ 
or  the  same  as  the  conclusion.,  or  result  in  a  coti- 
elusion  different  from  the  one  required.  If  so 
it  is  a  material  fallacy. 

SECTION   I. 

LOGICAL   FALLACIES. 

9.  It  is  evident  that  logical  fallacies  are  aa 
numerous  as  are  the  ways  of  violating  the  five 
rules  of  syllogism. 

Most  of  those  made  by  ambiguous  terms  may 
be  classified  as  follows : 

10.  I.  The  Fallacy  of  Equivocation,  arising 
from  an  equivocal  word,  or  from  the  ambiguous 
structure  of  the  sentence. 

This  class  will  be  found  to  violate  the  first 
rule  of  syllogism  ;  as, 

All  that  believe  shall  be  saved ; 

The  devils  believe ; 

Therefore,  the  devils  shall  be  saved. 

Every  one  desires  happiness; 

Virtue  is  happiness ; 

Therefore,  every  one  desires  virtue. 


LOGICAL   FALLACIES.  09 

In  the  first  example  the  term  believe  is  equiv 
ocal,  having  two  different  senses.  There  is, 
therefore,  in  reality,  two  terms ;  and  the  syllo- 
gism, consequently,  has  four  terms,  which  is  con- 
trary to  Eule  I  of  syllogisms.  In  the  second 
example  the  minor  premise  is  ambiguous. 

11.  II.  The  Fallacy  of  Similar  Expression 
arises  from  words  that  are  derived  from  the 
same  root  and  are  similar  in  sound,  but  not  in 
sense;  such  as  art,  artful;  faith,  faithful,' 
design,  designing.     As, 

**^  Designing  men  should  be  avoided : 

^  This  man  has  many  designs ; 

^  Therefore,  he  should  be  avoided. 

Z  This  violates  Rule  I  of  syllogism,  for  there  are 

^       in  reality  four  terms. 

'S  12.  III.  The  Fallacy  of  Composition  or  Di- 

^  VISION  is  when  the  middle  term  is  used  collect- 
ively in  one  premise,  and  not  collectively,  but 
distributively,  in  the  other.     As, 

Two  and  three  are  even  and  odd ; 
Five  is  two  and  three; 
Therefore,  five  is  even  and  odd. 

Tliis  is  a  fallacy  of  composition.  Two  and 
three  is  the  middle  term,  and  it  is  used  distrib- 


100  ELFMENTS  OF  LOGIC. 

atively  in  the  major  premise,  and  collectively 
in  the  minor  premise.  Hence  there  are  properly 
four  terms  in  this  argument,  which  is  contrary 
to  Rule  I  of  syllogism. 

The  planets  are  seven ; 
Mercury  and  Venus  are  planets ; 
Therefore,  Mercury  and  Venus  are  seven. 

This  is  a  fallacy  of  division.  The  middle 
term  is  used  distributively  in  the  minor  premise, 
and  collectively  in  the  major. 

13.  lY.  The  Fallacy  of  Accident  is  when 
the  middle  term  is  understood  simply  and  as  to 
its  essence,  in  one  premise,  but  in  the  other  is  so 
used  as  to  imply  that  something,  which  does 
not  belong  to  it  essentially,  but  accidentally^  is 

taken  into  account  with  it.     As, 

» 

Whatever  is  bought  in  the  shambles  is  eaten  by  man ; 
Raw  meat  is  bought  in  the  shambles ; 
Therefore,  raw  meat  is  eaten  by  man. 

Here  the  middle  term  is  hought  in  the 
shambles^  and  it  is  used  in  the  minor  premise, 
as  considered  simply,  and  as  to  its  essence ;  but 
in  the  major  premise  it  should  be  understood  in 
connexion  with  something  else,  as,  when  prop 


LOGICAL  FALLACIES.  101 

efrby  cooked.  Hence,  four  terms  are  empJoyed 
in  reality  in  this  argument  which  violates  Rule  J 
of  sj^llogism. 

EXAMPLES. 

1.  ]^o  one  is  rich  who  has  not  enough ; 
No  miser  has  enough ; 
Therefore,  no  miser  is  rich. 

2.  All  that  glitters  is  not  gold  ; 
Tinsel  glitters ; 
Therefore,  tinsel  is  not  gold. 

3.  He  who  calls  you  a  man  speaks  truly ; 
He  who  calls  you  a  fool  calls  you  a  man  ■, 
Therefore,  he  who  calls  you  a  fool  speaks 

truly. 

4.  W"arm  countries  alone  produce  wine 
Spain  is  a  warm  country ; 
Therefore,  Spain  produces  wine. 

5.  What  we  eat  grew  in  the  fields; 
Loaves  of  bread  are  what  we  eat ; 
Therefore,  loaves  of  bread   grew  in   the 

fields. 
0.  What  is  universally  believed  is  true^ 
The  existence  of  a  God  is  true; 
Therefore,  the  existence  of  a  God  is  uni- 
versally believed. 


102  ELEMENTS  OF  LOGIC. 

7.  Whatever   is    universally   believed    must 

be  true ; 
The    immortality  of  the  soul  is  not  imi 

versally  believed ; 
Therefore,  it  is  not  true. 

9.  What  I  am  you  are  not ; 
But  I  am  a  man ; 
Therefore,  you  are  not. 


SECTIOlSr   II. 

MATERIAL  FALLACIES. 

14.  Material  fallacies  may  be  as  numerous  as 
errors  of  learning,  mistakes  of  judgment,  or 
willful  duplicity  can  make  them. 

The  most  common  may  bt  included  in  th^ 
following  classes: 

15.  I.  The  Fallacy  of  begging  the  ques- 
tion is  that  of  inferring  a  conclusion  from  pre- 
mises substantially  the  same  as  the  conclusion, 
or  depending  upon  the  conclusion ;  as  ivhen  we 
attempt  to  prove  a  thing  by  itself,  or  by  a 
synonymous  word,  or  by  something  which  is 
itself  to  be  proved  by  the  very  point  you  seek 
to  establish.     As, 


MATERIAL   FALLACIES.  103 

God  is  eternal,  because  he  is  without  beginning  or  end* 
Opium  produces  sleep  because  it  is  soporific. 
We  know  the  Scriptures  are  true  from  the  infallible 
testimony  of  the  Church,  and  we  know  the  Church  is  in- 
fallible by  the  declaration  of  the  Scriptures. 

The  last  example  is  what  is  called  reasoning 
kn  a  circle. 

16.  II.  The  Fallacy  of  false  assumption  is 
when  the  premises  are  unduly  or  unwarrant- 
ably assumed ;  as  when  we  attempt  to  prove  a 
thing  by  something  that  is  false,  or  unknown,  or 
partially  stated.     As, 

All  bodies  that  move  themselves  are  animated ; 
All  stars  and  heavenly  bodies  move  themselves ; 
Therefore,  the  stars  and  all  the  heavenly  bodies  are 
animated. 

Meteors  have  a  volcanic  origin  ; 

For  they  cannot  otherwise  be  accounted  for. 

"We  hold  this  doctrine  to  be  true  by  the  authority  of 
St  Paul  in  such  and  such  texts. 

This  is  a  fallacy,  if  these  texts  do  not  contain 
the  whole  of  the  apostle's  testimony  to  the  point 
in  question,  and  is  sometimes  called  the  fallacy 
of  partial  reference. 

17.  III.  The  Fallacy  of  mistaking  the  ques- 
noN  is  that  in  which  the  premises  are  such  as 


104  ELEMENTS  OF  LOGIC 

result  in  a  conclusion  diflPerent  from  the  one 
required,  but  apparently  the  same.     As, 

Alfred  the  Great  was  a  scholar ; 

For  he  founded  the  University  of  Oxford. 

18.  The  sophist  will  not  always  draw  out  the 
conclusion,  but  leave  it  to  be  inferred,  for  in 
that  case  its  irrelevancy  will  be  less  likely  to  be 
detected. 

19.  This  fallacy  is  often  conveyed  in  appeals 
to  prejudice,  to  the  passions,  or  to  personal 
considerations;  sometimes  in  the  form  of  ob- 
jections, and  sometimes  by  implication,  in  ar- 
guments, which  go  to  prove  a  part  of  what  is 
required.     As, 

Gentlemen  of  the  jury,  this  man  is  a  friend  to  the  rights 
of  the  people.     Will  you  convict  him  ? 

This  work  is  not  evangelical.  Look  at  the  statements 
made  in  the  eighth  chapter.  Are  these  warranted  by  the 
New  Testament  ? 

These  objections  are  many  and  weighty.  Can  such  a 
science  be  worthy  of  credit? 

EXAMPLES. 

1.  The  soul  occupies  the  whole  body,  for  if 
resides  in  every  member. 


MATERIAL   FALLACIES.  105 

2.  The  plant  is  capable  of  much  growth,  for 

it  has  great  vegetative  powers. 

3.  The  soul  suffers  dissolution  with  the  body 

at  death.  See  Ecc.  iii,  18,  19,  20 ;  Job 
xxxiv,  15 ;  Psa.  cxlvi,  3,  4. 

4.  The  Bible  cannot  be  the  rule  of  faith,  foi 

men  understand  it  very  differently. 

5.  We  may  expect  some  dreadful  disaster,  for 

the  sky  last  night  was  full  of  falling 
meteors. 

6.  The  appearance  of  strange   birds  flying 

south  in  the  highest  northern  latitudes 
which  have  been  explored,  and  of  float- 
ing plants,  as  well  as  men  who  declare 
by  signs  that  they  come  from  the  far 
north,  indicate  that  the  earth  is  concave 
about  the  poles,  and  the  interior  of  the 
earth  is  inhabited. 

7.  Mohammed  is  a  prophet,  for  the  Koran  de- 

clares it ;  and  the  Koran  is  true,  for  Mo- 
hammed received  it  from  God,  as  he 
affirms. 

8.  Whatever  is  contrary  to  experience  is  not 

to  be  believed. 
Miracles  are  contrary  to  experience ; 
Therefore,  miracles  are  not  to  be  believed 


106  ELEMENTS   OF    LOGIC. 

9.  Paul  was  not  a  Komaii  citizen,  for  he  was 

born  at  Tarsus  in  Cilicia. 

10.  Job  was  a  great  sinner,  for  he  was  over- 

whelmed with  great  calamities. 

11.  No  evil  should  be  allowed  that  good  maj^ 

come  of  it ; 
All  punishment  is  an  evil ; 
Therefore,  no  punishment  should  be  al 

lowed  that  good  may  come  of  it. 

12.  "Ho  man  can  possess  power  to  perform  an 

impossibility ; 
A  miracle  is  an  impossibility; 
Therefore,  no  man  can  possess  power  to 

perform  a  miracle. 

13.  Which  of  you  having  an  ox  or  an  ass  fall 

into  a  pit,  will  not  pull  him  out  on  the 
Sabbath  day? 
The  last  is  a  personal  appeal,  called  Ar- 
gumentum  ad  hominem,  and  is  allow- 
able when  your  object  is  to  silence  the 
captious.  As  offered  to  prove  the 
point  in  question,  it  is  a  fallacy.  (19.) 


SUPPLEMENT 


SECTION   I. 

MOODS  AND  FIGURES  OF  SYLLOGISMS 

This  subject  may  be  advantageously  studied 
after  the  scholar  has  become  perfectly  familiar 
with  the  foregoing,  and  is  expert  in  the  applica 
tion  of  all  the  rules  of  logic.  In  that  case  it 
may  serve  to  discipline  the  mind,  otherwise  it 
will  only  perplex.  One  may  be  an  able  logician 
without  the  doctrine  of  moods  and  figures. 

1.  The  Mood  of  a  Syllogism  is  the  deaigna 
tion  of  the  quantity  and  quality  of  its  proposi- 
tions. 

This  is  done  by  the  symbols  A,  E,  I,  and  O, 
which  stand  respectively  for  the  universal  al 
tirmative,  universal  negative,  particular  affirma- 
tive, and  particular  negative. 


108  ELEMENTS  OF  LOGIC. 

Tlie  following,  for  example,  is  A,  A,  A 

A.     All  animals  are  mortal; 

A.     All  men  are  animals ; 

A.    Therefore,  all  men  are  mortal 

The  following  is  E,  A,  E. 

E.  No  human  invention  is  perfect ; 
A.  Language  is  a  human  invention 
E.    Therefore,  no  language  is  perfect. 

2.  The  whole  number  of  the  moods  of  valid 
syllogisms  is  only  eleven.  A,  A,  A, — A,  A,  I, — 
A,  E,  E,— A,  E,  O,— A,  I,  I,— A,  O,  O,— E,  A, 
E,— E,  A,  O,— E,  I,  0,-1,  A,  1,-0,  A,  O 

3.  As  there  are  sixty-four  different  ways  in 
which  it  is  possible  for  A,  E,  I,  O  to  be  com- 
bined to  form  a  syllogism,  there  might  be  fifty- 
three  other  moods  formed,  as  E,  E,  A, — I,  I,  I, 
etc. ;  but  they  would  offend  against  one  or  more 
^f  the  five  rules  of  syllogism.     As, 

L    Some  birds  are  animals ; 

I.     Some  fish  are  animals ; 

I.    Therefore,  some  fish  are  birds. 

E.     No  human  invention  is  perfect ; 

E.    No  language  is  perfect ; 

A.     Therefore,  language  is  a  human  invention. 


MOODS  AND  FIGURES  OF  SYLLOGISMS.      109 

These  examples  are  contrary  to  the  fifth  rule 
of  syllogisms.  Two  negative  or  two  particular 
premises  prove  nothing. 

4.  The  Figure  of  a  Syllogism  denotes  the 
situation  of  the  middle  term,  in  respect  to  the 
major  and  minor  terms. 

5.  Figure  First  is  when  the  middle  term  is 
the  subject  of  the  major  premise  and  the  pre- 
dicate of  the  minor  premise.     As, 

A.    Every  wicked  man  is  miserable ; 

A.    Every  tyrant  is  a  wicked  man ; 

A.    Therefore,  every  tyrant  is  miserablev 

E.     No  discontented  man  is  a  happy  man ; 
A.    Every  wicked  man  is  a  discontented  man ; 
E.    Therefore,  no  wicked  man  is  a  happy  man. 

A.    All  the  faithful  are  dear  to  God; 
I.    Some  that  are  afflicted  are  faithful ; 
I.    Therefore,  some  that  are  afflicted  are  dear  to  God. 

E.     No  virtue  is  an  evil ; 
I.     Some  difficult  things  are  virtues ; 
O.    Therefore,  some  difficult  things  are  not  evils. 

6.  To  this  figure  the  logical  axiom  applies 
directly  ;  and  to  this  figure  all  the  other  figures 
may  be  reduced. 


no  ELEMENTS  OF   LOGIC. 

\M,  Figure  Second  is  when  the  middle  term  is 
jJ^G  predicate  of  both  the  major  and  the  minor 
if  jpremises ;  as, 

xr      E.    No  happy  man  is  discontented ; 

/A.    Every  wicked  man  is  discontented ; 
vV        E^y^Therefore,  no  wicked  man  is  a  happy  man. 

xA..    Every  wicked  man  is  discontented  i 
L  ^.    No  happy  man  is  discontented ; 

y  Jfe.    Therefore,  no  happy  man  is  a  wicked  man. 

.   f^       ^    E.    No  evil  is  a  virtue; 
y    Vs        I.    Some  difficult  things  are  virtues ; 

().    Therefore,  some  difficult  things  are  not  evils. 

A.    Every  good  man  is  afflicted:/ 

0.     Some  rich  men  are  not  afflicted ; 

0.     Therefore,  some  rich  men  are  not  good  men. 

8.  Figure  Thisd  is  when  the  middle  term  is 
the  subject  of  both  the  premises.     As, 

A.    All  the  faithful  are  dei\r  to  G-od ; 
A,    All  the  faithful  are  aMicted ; 
I.    Therefore,  some  that  are  afflicted  are  dear  to  God. 

I.  Some  of  the  faithful  are  afflicted ; 
A.  All  the  faithful  are  dear  to  God ; 
I.    Therefore,  some  that  are  dear  to  God  are  afflicteil 


MOODS  AND  FIGURES  OF  SYLLOGISMS.      Ill 

A,    All  the  faithful  are  dear  to  God ; 
r.    Some  of  the  faithful  are  aflQicted ; 
L    Therefore,  some  that  are  afflicted  are  dear  to  God 

El     No  virtue  is  an  evil ; 

A.    All  virtues  are  difficult ; 

O.    Some  difficult  things  are  not  evils. 

O.    Some  called  Christians  are  not  true  believers ; 
A.    All  called  Christians  profess  faith ; 

0.  Therefore,   some  who  profess  faith  are  not  true 
Delievers. 

E.    No  virtue  is  an  evil ; 
I.     Some  virtues  are  difficult. 
O.     Therefore,  some  difficult  things  are  not  evils. 

9.  Figure  Fourth  is  when  the  middle  term  is 
the  predicate  of  the  major  and  the  subject  of 
the  minor  premise. 

10.  This  is  the  reverse  of  the  first  figure  and 
is  the  most  awkward  of  all.     As, 

A.    Every  tyrant  is  a  wicked  man ; 
A.    Every  wicked  man  is  miserable , 

1.  Therefore,  some  that  are  miserable  are  tyrants. 

A ,    Every  wicked  man  is  discontented ; 

E.     No  disomtented  man  is  happy; 

E.    Therefore,  no  happy  man  is  a  wickcq  man. 


112  ELEMENTS  OF    LOGIC. 

I.    SoDic  afflicted  are  faithful ; 
A.     All  the  faithful  are  dear  to  God ; 

I.  Therefore,  some  that  are  dear  to  God  are  alBicled. 

E.    No  evil  is  a  virtue ; 

A.     All  virtues  are  difficult ; 

0.    Therefore,  some  difficult  things  are  not  evils* 

E.    No  evil  is  a  virtue ; 
I.    Some  virtues  are  difficult ; 
O.     Therefore,  some  difficult  things  are  not  evils. 

II.  Each  of  the  eleven  allowable  moods  will 
not  go  in  every  figure,  for  it  will  violate  some 
of  the  rules  of  syllogism  in  one  figure,  though 
not  in  another.  For  example.  A,  A,  A,  which 
goes  in  the  first  figure  will  not  go  in  the  third 
figure. 

Figure  1st.  All  wicked  men  are  miserable ; 
All  tyrants  are  wicked  men ; 
Therefore,  all  tyrants  are  miserable. 

Figure  8d.  All  wicked  men  are  miserable ; 
All  wicked  men  are  tyrants ; 
Therefore,  all  tyrants  are  miserable. 

This  violates  Kule  III  of  syllogism,  for  the 
term  tyrants  is  distributed  in  the  conclusion, 
though  not  in  the  premises.  Besides,  the  minor 
premise  is  incorrect. 


MOODS  AND  FIGURES  OF  SYLLOGISMS.      113 

12.  Some  of  the  moods,  also,  which  might  be 
admitted  in  some  of  the  figures  are  useless,  as 
having  a  particular  conclusion  when  the  uni- 
versal might  be  drawn. 

For  example.  A,  A,  I  will  go  in  the  fourth 
figure,  but  in  the  first  figure  it  is  useless. 

Figure  4th.  A.  Every  tyrant  is  a  wicked  man ; 

A.  Every  wicked  man  is  miserable ; 

I.  Therefore,  some  that  are  miserable  are 
tyrants. 

Figure  Ist.  A.  Every  wicked  man  is  miserable ; 

A.  Every  tyrant  is  a  wicked  man ; 

A.  Therefore,  every  tyrant  is  miserable. 


But, 


I.    Therefore,  some  tyrants  are  miserable; 


would  be  a  useless  conclusion,  for  a  universal 
conclusion  is  legitimate. 

13.  For  these  reasons,  out  of  the  forty-four 
allowable  moods,  which  mighty  possibly  go  into 
the  four  figures,  only  nineteen  are  retained. 
Examples  of  all  the  nineteen  are  found  above 
unier  the  definitions  of  the  four  figures. 

14.  To  assist  in  remembering  these  moods, 
and  the  figure  in  which  they  are  found,  the  fol- 
lowing mnemonic  lines  have  been  invented : 


114  ELEMENTS  OF  LOGIC. 

First.     bArbA'rA,  cElA'rEnt,  dArll,  f Erl'O. 
SecoTid.  cEsA'rE,  cAmE'strEs,  f Estl'iiO,  bArC/kO. 
Third,   dArA'ptI,    dlsA'inls,    dAtl'sI,    fElA'ptOn, 

bOkA'rdO,  f Erl'sO. 
Fourth.  brAmA'ntlp,  cAmE'nEs,  dIraA'rIs,  fEsA'pO, 
frEsI'sOn. 

Here,  it  will  be  seen,  are  only  ten  moods, 
but  some  are  employed  in  more  than  one  figure, 
as  E,  1,  O,  making  nineteen  in  all  the  four 
figures. 

15.  If  any  syllogism  be  not  found  in  these 
lines  it  cannot  be  a  valid  syllogism ;  it  is  a 
logical  fallacy. 

16.  The  utility  of  the  mnemonic  lines  is  like 
that  of  duly  certified  weights  and  measures,  by 
which  we  test  the  size  or  weight  of  bodies  with- 
out the  necessity  of  a  minute  and  tedious  calcu- 
lation. 

SECTION    II. 

REDUCTION. 

17  The  process  by  which  the  moods  of  the 
last  three  figures  are  changed  into  a  mood  of 
the  first  figure  is  called  Heduction. 

18.  This  is  done  in  two  ways;  by  Ostensive 
Reduction  and  by  E-eductio  ad  impossibile. 


REDUCTION.  1 16 

19.  OsTENSivE  Eeduction  is  performed  by 
the  conversion  of  one  of  the  premises,  A  into 
r,  E  into  E,  I  into  I,  and  bv  transposing  the 
premises  when  occasion  requires. 

For  example,  take  Cesare  of  the  second 
figure. 

cEs.     No  happy  man  is  discontented ; 
A.    Every  wicked  man  is  discontented; 
rE.    Therefore,  no  wicked  man  is  a  happy  man. 

This  may  be  converted  into  Celarent  of  the 
first  figure  by  the  simple  conversion  of  the 
major  term,  thus: 

cE.     No  discontented  man  is  a  happy  man ; 
lA.    Every  wicked  man  is  a  discontented  man ; 
rEnt.    Therefore,  no  wicked  man  is  a  happy  man. 

Take  now  Camestres  of  the  second  figure  and 
convert  that  also  into  Celarent.  To  do  this  you 
will  only  have  to  convert  the  minor  premise 
and  transpose  the  premises,,  as  will  be  seen  in 
the  following  examples. 

cAm.     Every  wicked  man  is  discontented ; 
Es.    No  happy  man  is  discontented;  {convert  and 
transpose.) 
trEs.     Therefore,  no  happy  man  is  a  wicked  man 


il6  ELEMENTS  OF  LOGIC. 

cE.    No  discontented  man  is  a  happy  man ; 
lA.    Every  wicked  man  is  discontented  ; 
rEnt.    Therefore,  no  wicked  man  is  a  happy  man. 

20.  In  like  manner  all  the  moods  of  the  lasf 
three  figures  can  be  reduced  into  one  of  the  four 
perfect  moods  of  the  first  figure. 

21.  In  the  mnemonic  lines  the  initial  letters 
b^  G,  d^  y,  show  to  which  mood  of  the  first  figure 
the  reduction  is  made,  namely,  harhara^  celarent^ 
darii,  or  ferio.  The  letter  m  signifies  that  the 
premises  are  to  be  transposed,  as  above,  in 
Camestresj  the  letter  s  denotes  that  the  propo- 
sition, which  the  preceding  vowel  stands  for,  is 
to  be  converted  by  simple  conversion,  and  jp, 
by  particular  conversion ;  but  p  in  Bramomtvp 
marks  that  the  premises,  when  changed,  warrant 
a  universal  conclusion  instead  of  a  particular. 
The  symbols  A  E  I  O  mark  the  moods,  that  is, 
the  quality  or  quantity  of  the  propositions. 

22.  Reductio  ad  Impossibile  is  when  you 
reduce  a  mood  to  the  first  figure,  by  substitut- 
ing the  contradictory  of  the  conclusion  for  one 
of  the  premises ;  by  which  an  absurdity  follows 
which  proves  not  directly  that  the  conclusion  is 
true,  but  that  it  cannot  be  false. 

Thus  Baroko^  in  the  second  figure. 


REDUCTION.  117 

b Ar.    Every  good  man  is  afflicted ; 
Ok.     Some  rich  men  are  not  afflicted; 
O.    Therefore,  some  rich  men  are  not  good  men. 

bAr.  Every  good  man  is  afflicted ; 
bA.  All  rich  men  are  good  men ; 
r  A.    Therefore,  all  rich  men  are  afflicted. 

Which  conclusion  is  notoriously  false,  and  the 
original  conclusion  which  you  had  drawn  is, 
therefore,  true. 

23.  The  letter  Jc  in  the  mnemonic  lines  de- 
notes that  the  proposition  indicated  by  the 
vowel  immediately  preceding  is  to  be  substi- 
tuted by  the  contradictory  of  the  conclusion ; 
the  other  letters,  not  above  explained,  have  no 
signification. 

EXAMPLES. 

1.  Whoever  has  reflection  and  volition  has 

the  essential  properties  of  mind ; 

Mankind  has  reflection  and  volition  ; 

Therefore,  mankind  has  the  essential  prop- 
erties of  mind. 

2.  Whatever  is  universally  believed  must  be 

true ; 
The  existence  of  God  is  not  universally 

believed ; 
Therefore,  it  is  not  true. 


118  ELEMENTS   OF   LOGIC. 

3.  Whoever  is  capable  of  deliberate  crime  is 

responsible ; 
An   infant   is   not   capable   of    deliberate 

crime ; 
Therefore,  an  infant  is  not  responsible. 

4.  Some  philosophers  reckon  virtue  good  in 

itself ; 

The  Epicureans  did  not  reckon  virtue  good 
in  itself; 

Therefore,  the  Epicureans  were  not  phil- 
osophers. 

5.  Prudence  has  for  its  object  the  benefit  of 

individuals; 
But  prudence  is  a  virtue ; 
Therefore,  some  virtue  has  for  its  object 

the  benefit  of  individuals. 

6.  Whatever  is  expedient  is  conformable  to 

nature. 
.  Whatever  is  conformable  to  nature  is  not 
hurtful  to  society. 
Therefore,  what   is    hurtful   to   society  is 
never  expedient. 

7.  No  man  is  happy  who  is  not  secure ; 
No  tyrant  is  secure; 

Therefore,  no  tyrant  is  happy. 


EXAMPLES.  119 

S.  All  true  patriots  are  friends  to  religion  ; 
Some  great  statesmen  are  not  friends  to 

religion ; 
Therefore,  some  great  statesmen  are  not 

true  patriots. 

9.  All  true  Christians  have  peace ; 

Some  afflicted  men  are  true  Christians ; 
Therefore,  some  afflicted  men  have  peace. 

10.  No  uncandid  man  is  fit  to  reason  correctly; 
Some  infidels  are  uncandid ; 
Therefore,   some   infidels    are    not   fit    to 

reason  correctly. 

11.  E,  E,  E,— I,  O,  0,—I,  E,  O. 

12.  I,  A,  I,— A,  E,  E,  in  the  first  figure. 

13.  A,  A,  A  in  the  third  figure,  A,  E,  O. 


120  ELEMENTS  OF   LOGIC. 


QUESTIONS  IN  A  GENERAL  REVIEW. 

1 .  What  is  Logic  ? 

2.  What  does  it  assume  as  its  foundation  ? 

3.  What  are  first  truths  ? 

4.  What  are  first  principles  ? 

5.  What  is  the  true  process  of  reasoning  ? 

6.  What  is  Aristotle's  dictum  ? 

7.  What  is  a  distributed  term  ? 

8.  What  are  the  rules  of  distribution? 

9.  What  is  opposition? 

10.  What  is  conversion  ? 

11.  What  two  canons  have  logicians  invertoc 

to  test  the  validity  of  arguments  ? 

12.  What  five  rules  must  be  observed  ? 

13.  What  are  hypothetical  syllogisms? 

14.  What  two  kinds  of  these? 

15.  Can  they  be  reduced  to  one? 

16.  Can  they  be  reduced  to  categoricals  ? 
IT.  What  is  a  dilemma. 

18.  What  is  the  special  advantage  of  it? 

19.  What     distinctions    of     reasoning     art 

found  ? 

20.  Are  these  different  in  principle? 

21.  What  division  of  fallacies  is  made? 


APPE^  DIX, 


THE  PHILOSOPHY  OF  INDUCTION.* 

It  has  long  been  the  fashion  to  decry  the 
logic  of  Aristotle,  because,  its  legitimate  use 
not  being  understood  in  the  medieval  schools, 
it  served  to  divert  the  minds  of  men  from  the 
study  of  nature,  and  set  them  whirling  about  in 
dialectic  circles  to  educe  the  principles  of  science 
and  the  laws  of  the  universe ;  and  Bacon  and 
Des  Cartes  have  been  lauded  to  the  skies,  be- 
cause they  taught  that  nature  reveals  her  laws 
only  in  the  passing  phenomena  of  matter  and 
mind,  as  presented  to  the  senses  and  the  con- 
sciousness, which  must   be   carefully  analyzed 

•First  delivered  before  the  Philosophical  Society  of  Dickinson 
College.    1853. 


122  ELEMENTS  OF   LOGIC. 

and  then  generalized  by  the  process  of  induction, 
A  comparison  has  been  made  between  the  or- 
ganon  of  Aristotle  and  the  organon  of  Bacon, 
or,  to  speak  more  precisely,  between  the  method 
of  deduction  and  of  induction,  altogether  to  the 
disparagement  of  the  former,  until  at  length  it 
has  come  to  pass  that  it  is  no  longer  regarded 
by  many  as  of  vital  importance  to  scientific  in- 
vestigation, while  induction  is  considered  as  not 
merely  an  indispensable  auxiliary  to  the  dis- 
covery of  new  truths  and  principles,  but  as  the 
only  fundamental  process  of  inference — the 
ouly  process  by  which,  from  facts  perceived  by 
the  intelligence,  you  can  advance  to  the  determ- 
ination of  the  laws  and  principles  which  are 
the  objects  of  science. 

It  is  remarkable  that,  notwithstanding  the 
exaltation  of  induction,  since  Bacon  directed 
the  attention  of  philosophers  to  it,  no  thorough 
attempts  were  made  to  expound  its  philosophy 
and  to  institute  its  canons  until  very  recently.. 
Dr.  Whewell,  Mr.  John  Stuart  Mill,  Dr.  Henry 
Tappan,  and  Sir  William  Hamilton,  and  writers 
in  other  tongues,  have  supplied  the  desideratum 
by  works  profoundly  investigating  the  whole 
subject  of   logic,  and    particularly   induction. 


THE   PHILOSOPHY   OF  INDUCTION.  12b 

We  have,  therefore,  the  means  by  which  we 
may  sit  in  judgment  upon  the  question  and 
rendei  an  enlightened  verdict. 

COUSIN'S  VIEW  OF  INDUCTION. 

The  particular  aspect  of  the  question  which 
It  is  the  design  of  this  paper  to  examine,  is 
clearly  presented  in  the  following  remarks  in 
Cousin's  critique  of  the  philosophy  of  Locke. 
Cousin  wonders,  as  well  he  may,  that  a  leader 
in  the  sensual  and  Baconian  school  of  philoso- 
phy should  so  far  be  warped  from  his  appropri- 
ate sphere  of  thought  as  to  lose  sight  altogether 
of  induction  as  one  of  the  legitimate  modes  of 
knowledge,  while,  at  the  same  time,  casting 
contempt  upon  the  syllogism  as  the  proper  type 
of  the  reasoning  process ! 

"Thus  intuition  and  demonstration  are  the 
different  modes  of  knowledge,  according  to 
Locke.  But  are  there  no  others?  Have  we 
not  knowledge  which  we  acquire  neither  by 
intuition  nor  demonstration?  How  do  we  ac- 
quire a  knowledge  of  the  laws  of  external 
nature?  Take  which  you  please,  gravitation  for 
instance.  Certainly  there  is  no  simple  intuition 
and  immediate  evidence  here,  for  experiments 


124  ELEMENTS  OF  LOGIC. 

multiplied  and  combined  are  necessarj  to  give 
the  slightest  law ;  and  even  this  will  not  snilice, 
since  the  slightest  surpasses  the  number,  what- 
ever it  be,  of  experiments  from  which  it  is 
drawn.  There  is  need,  therefore,  of  an  inter- 
vention of  some  other  operation  of  mind  besides 
intuition.  Is  it  demonstration?  Impossible,  for 
demonstration  is  the  perception  of  the  relation 
between  two  ideas  by  means  of  a  third  ;  but  it 
is  upon  the  condition  that  the  latter  should  be 
more  general  than  the  two  others,  in  order  to 
embrace  and  connect  them.  To  demonstrate 
is,  in  the  last  analysis,  to  deduce  the  particular 
from  the  general.  Now,  what  is  the  more  gen- 
eral physical  law  from  which  gravitation  can  be 
deduced  ?  We  have  not  deduced  the  knowledge 
of  gravitation  from  any  other  knowledge  an- 
terior to  it,  and  which  involves  it  in  the  germ. 
How,  then,  have  we  acquired  this  knowledge, 
wliich  we  certainly  have  ?  and,  in  general,  how 
do  we  acquire  the  knowledge  of  physical  laws? 
A  phenomenon  having  been  presented  a  num* 
ber  of  times,  with  a  particular  character  and  in 
particular  circumstances,  we  have  judged  that 
if  this  same  phenomenon  should  occur  in  similar 
circumstances,  it  would  have  the  same  character; 


THE   PHILOSOPHY    OF   INDUCTION.         125 

that,  is  to  say,  we  have  generalized  the  particular 
character  of  this  phenomenon.  Instead  of  de- 
scending from  the  general  to  the  particular,  we 
have  ascended  from  the  particular  to  the  gen- 
eral. This  general  character  is  what  we  call  a 
law :  this  law  we  have  not  deduced  from  a  more 
general  law  or  character;  we  have  derived  it 
from  particular  experiments  in  order  to  transfer 
it  beyond  them.  It  is  not  simple  resumptior 
nor  a  logical  deduction ;  it  is  what  we  call  in- 
duction. It  is  to  induction  that  we  owe  all 
conquests  over  nature,  all  our  discoveries  of  the 
laws  of  the  world." 

PEOBLEM   TO   BE    SOLVED. 

This  clear  and  eloquent  exposition  of  the 
order  of  thought  in  the  two  processes  of  deduc- 
tion and  induction,  as  it  has  commonly  been 
apprehended,  enables  us  to  present,  without 
danger  of  being  misunderstood,  the  problem 
which  we  wish  to  solve,  namely,  that  there  is 
no  fundamental  difference  between  induction 
and  deduction ;  but  in  both  cases  the  mind  pro- 
ceeds from  the  more  general  to  the  less  general, 
or  from  the  general  to  the  particular ;  and  that 
the  opposite   process  of  proceeding   from    the 


126  ELEMENTS   OF   LOGKJ. 

particular  to  the  general  is  utterly  inipossible. 
All  inference,  I  maintain,  is  of  one  kind— -it  is 
deductive.  You  may  take  as  many  particulars 
as  you  can  gather  together,  and  they  will  be 
perfectly  barren  of  any  consequence,  unless  you 
can  attach  them  to  a  general  principle.  Yon 
may  sum  them  up  and  call  it  generalization, 
but  you  can  never  infer  a  universal  law,  you 
can  make  no  scientific  generalization  by  means 
of  them,  unless  you  can  put  them  upon  some 
broader  general  principle  than  that  which  you 
wish  to  educe  from  them.  Take  the  instance 
of  scientific  induction  referred  to  by  Cousin, 
that  of  the  law  of  gravitation,  and  analyze  it 
thoroughly,  and  you  will  see  that  it  is  at  bottom 
deduction.  A  philosopher  observes  a  material 
substance — a  body — say,  an  apple,  fall  to  the 
ground ;  he  observes  another  body,  a  leaf,  in 
like  manner  disengaging  itself  from  the  ^ree 
and  following  the  apple ;  he  casts  a  stone  into 
the  air,  it  takes  the  same  direction ;  he  casts  a 
feather  upon  the  winds,  and,  though  for  a  time 
it  is  resisted  by  the  currents  of  air,  yet,  when 
these  obstacles  cease,  it  directly  in  like  manner 
falls  to  the  earth.  From  these- particulars  he 
observes  that  it  is  the   material  substance  in 


THE   PHILOSOPHY  OF   INDUCTION.  127 

Lhese  different  bodies  that  exliibits  the  phe- 
nomenon of  falling  to  the  earth,  and  not  any 
particular  qualit}'  of  the  apple,  or  the  leaf,  or 
the  Stone,  or  the  feather;  and  this  is  his  analysis. 
Thereupon  he  proceeds  to  infer  that  all  bodies — 
all  material  substances — in  all  parts  of  the  globe 
will  behave  in  like  manner ;  in  other  words,  he 
infers  the  law  of  terrestrial  gravity.  This  is  his 
induction.  He  seems,  indeed,  merely  to  pro- 
ceed from  the  particular  to  the  general ;  but 
how?  by  what  authority?  on  what  ground?  To 
answer  this  question  is  to  solve  the  problem  of 
induction. 

DE.   WHEWELL'S    SOLUTION. 

Di  Whewell,  who  has  elaborated  this  point, 
says  that  the  conclusion  is  not  a  mere  summing 
up  of  these  particulars,  and  of  all  known  par- 
ticulars of  the  same  nature ;  it  is  something 
more,  a  conception  which,  while  it  expresses 
these  particulars,  transcends  them ;  it  reaches 
all  possible  cases  of  the  same  kind.  But  how 
do  we  get  this  conception  ?  He  says  we  leap  to 
it:  "Induction  mounts  the  ladder  by  a  leap, 
which  is  out  of  the  reach  of  method."  But 
then  it  can  turn  round  and  verify  itself  by  de- 


128  ELEMENTS  OF   LOGIC. 

scending  the  ladder,  step  by  step,  by  the  de- 
ductive process.  But  how  do  we  make  the 
leap?  By  a  sort  of  philosophical  "sagacity — 
a  scientific  instinct — "  which  is  the  rare  gift 
of  some  superior  minds.  But  this  explains 
nothing. 

ANALYSIS  OF  INDUCTION,   BY  J.   S.   MILL. 

Now,  if  this  inference  of  the  general  law 
from  observed  particulars  be  a  legitimate  pro- 
cedure, and  it  cannot  admit  of  any  solution, 
then  it  must  be  regarded  as  ultimate,  and  we 
may  call  it  induction,  and  mark  it  as  the  oppo- 
site of  deduction.  But  it  happens  that  we  can 
analyze  the  process  in  this  instance  and  in  all 
instances  of  induction ;  and  this  analysis  will 
show  that  the  subtle  movement  of  the  reasoning 
faculty  from  the  particulars  to  the  general  is 
upon  the  broad  basis  of  a  universal  and  intuitive 
principle ;  and  thus  the  whole  process  could 
easily  be  put  into  the  form  of  a  syllogism, 
with  the  principle  for  its  major  premise, 
and  these  observed  particulars  for  its  minor 
premise. 

Happily  the  desired  analysis  of  this  process  is 
furnished  to  our  hand  by  Mr.  Mill,  who  not  only 


THE   PHILOSOPHY   OF  INDUCTION.  129 

goes  with  Cousin  in  maintaining  that  induction 
is  one  fundamental  mode  of  investigation,  but 
advances  far  beyond  him,  contending  with  great 
ability  that  inference  is  always  fundamentally 
from  particulars  to  generals,  and  that  deduction 
is  only  an  intermediary  process,  which  may  be 
resorted  to  for  convenience,  but  is  of  no  avail 
for  original  discovery. 

And  here  I  can  scarcely  refrain  from  remark- 
ing how  happily  opposite  systems  conspire  to 
advance  the  light  of  truth!  By  their  conflict 
they  bring  to  view  the  vital  points  of  inquiry, 
and  clear  the  ground  for  those  who  would  ap- 
proach to  determine  the  merits  of  the  case.  If 
Mr.  Mill  has  taken  the  wrong  side  of  this  ques- 
tion, yet  it  will  ever  be  to  his  praise  that  his 
thorough  comprehension  of  the  subject  and  his 
precise  and  candid  statements  have  placed  the 
controversy  in  the  clearest  light;  and  if  logicians 
differ  it  will  not  be  because  the  point  in  dis- 
pute is  misapprehended,  but  because  their  dif- 
ferent systems  of  philosophy  drive  them  to  op- 
posite conclusions.  Hear  what  he  says :  "  We 
must  first  observe  that  there  is  a  principle  im- 
plied in  the  very  statement  of  what  induction 

is,  an  assumption  with  regard  to  the  course  of 
9 


180  ELEMENTS  OF   LOGIC. 

nature  and  the  order  of  the  universe  ;  namely , 
that  there  are  such  things  as  parallel  cases,  that 
what  happens  once  will  happen  again,  and  not 
only  again  but  always." — YoL  i,  p.  370. 

It  is  evident  that  Mr.  Mill  has  thoroughly 
elaborated  the  opinion,  for  he  has  profoundly 
criticised  the  statement  of  it  as  made  by  Reid 
and  Stewart,  namely,  that  it  is  an  intuitive  con- 
viction that  the  future  will  be  as  the  present. 
He  remarks :  "  Time,  in  its  modification  of  past, 
present,  or  future,  has  nothing  to  do  either  with 
tho  belief  itself  or  the  grounds  of  it.  We  be- 
lieve that  fire  will  burn  to-morrow,  because  it 
burned  to-day  and  yesterday ;  but  we  believe 
on  precisely  the  same  grounds,  that  it  burned 
before  we  were  born,  and  that  it  burns  at  this 
very  day  in  Cochin  China.  It  is  not  from  the 
past  to  the  future,  as  past  and  future,  that  we 
infer,  but  from  the  known  to  the  unknown,  from 
facts  observed  to  facts  unobserved,  from  what 
we  have  perceived  or  have  been  directly  con- 
Bcious  of,  to  what  has  not  come  within  our  ex- 
perience. In  this  last  predicament  is  the  whole 
region  of  the  future,  but  also  the  vastly  greater 
portion  of  the  present  and  the  past." 


THE  PHILOSOPHY   OF   INDUCTION.  131 


THE  ERROR  OF   MILL. 

Thus  far  his  criticism  is  just ;  but  in  whai 
follows  he  denies  that  this  principle  is  intuitive, 
and  herein  lies  the  whole  error  of  his  system. 
His  empiricism  forbids  him  to  acknowledge  that 
any  universal  principles,  even  the  first  principles 
of  mathematics,  are  intuitive.  Hesays:  '•  What- 
ever be  the  most  proper  mode  of  expressing  it, 
the  proposition  that  the  course  of  nature  is  uni- 
form, is  the  fundamental  principle  or  general 
axiom  of  induction.  It  would  yet  be  a  great 
error  to  consider  this  large  generalization  as  any 
explanation  of  the  inductive  process.  On  the 
contrary,  I  hold  it  to  be  an  instance  of  induc- 
tion, and  induction  by  no  means  of  the  most 
obvious  kind.  Far  from  being  the  first  induc- 
tion we  make,  it  is  one  of  the  last,  or,  at  all 
events,  one  of  those  which  are  latest  in  attain- 
ing strict  philosophical  accuracy.  As  a  general 
maxim,  indeed,  it  has  scarcely  entered  the 
minds  of  any  but  philosophers,  nor  even  by 
them,  as  we  shall  have  many  opportunities  of 
remarking,  have  its  extent  and  limits  been  al- 
ways justly  conceived.  It  is  this  principle, 
thougU  so  far  from  being  our  earliest  induction, 


182  ELEMENTS  OF    LOGIC. 

wh.»cli  must  be  considered  as  our  warrant  for  all 
others  in  this  sense,  that  unless  it" were  true,  all 
other  inductions  would  be  fallacious." 

Thus  this  ingenious  reasoner  disclaims  what 
he  at  first  seemed  to  affirm.  He  disclaims 
making  this  principle  any  explanation  of  the 
process  of  induction  as  being  founded  upon  it, 
or  proceeding  through  it ;  but  he  now  regards 
it  as  only  the  sine  qua  non  of  correct  induction, 
so  that  no  induction  could  be  valid  were  its 
truth  not  admitted!  And  why?  Because  he 
thinks  this  principle  is  itself  an  induction,  and 
that  not  the  earliest  in  science.  But  if  so,  how 
could  the  earliest  inductions  have  been  made  if 
their  truth  depends  wholly  upon  this  as  their 
"fundamental  principle?"  And  if  itself  be  an 
induction  how  could  it  be  made  at  all  ?  It  then 
must  have  been  founded  upon  itself,  or  else 
here  is  one  induction,  and  that  the  greatest  of 
all,  which  is  not  formed  on  this  principle.  Good 
reason  in  these  paralogisms  to  modify  his  state- 
ment! But  take  his  qualified  statement,  that 
this  late  induction  is  the  warrant  of  all  other 
inductions,  then  it  follows  that  all  scientific  in- 
ductions up  to  the  time  when  this  was  formed, 
were  without  any  warrant ;   and  that  warrant 


THE  PHILOSOPHY   OF  INDUCTION.         133 

itself  is  without  any  warrant,  except  it  be  war- 
ranted by  itself;  and  if  this  be  impossible,  then 
itself  and  all  other  inductions  warranted  by  it 
are  without  authority  I 

But  if  we  read  on  we  shall  find  that  what  he 
calls  "warrant  in  a  certain  sense"  is  what  all 
who  believe  in  deductive  reasoning  will  call 
proof:  "Archbishop  Whately  has  well  remarked 
that  every  induction  is  a  syllogism,  with  the 
major  premise  suppressed ;  or,  as  I  prefer  to 
express  it,  that  every  induction  may  be  thrown 
into  the  form  of  a  syllogism  by  supplying  a 
major  premise.  If  this  be  actually 'done,  the 
principle  which  we  are  now  considering,  that 
of  the  uniformity  of  the  course  of  nature,  will 
appear  as  the  ultimate  major  premise  of  all  in- 
ductions, and  will,  therefore,  stand  to  all  in- 
ductions in  the  relation  in  which,  as  has  been 
shown  at  so  much  length,  the  major  premise 
always  stands  to  the  conclusion,  not  coni/i^ibutr 
mg  at  all  to  jprove  it^  but  being  a  necessary  con- 
dition of  its  being  proved,  since  no  conclusion 
is  proved  in  which  there  cannot  be  found  a  true 
major  premise." 

But  why  will  not  Mr.  Mill  allow  that  a  true 
major  premise  of  a  true  syllogism  proves  its  cod- 


184  ELEMENTS  OF   LOGIC. 

elusion ?  Because  the  major  premise  contains  the 
conclusion,  and  itself  was  formed  by  the  addition 
of  particulars,  or  induction  from  particulars  of 
which  that  very  conclusion  was  one.  Passing 
this  for  the  present,  it  is  enough  for  our  purpose 
that  he  admits  that  the  principle  of  the  uniform 
course  of  nature  is  the  foundation  of  every  in- 
duction in  the  very  tjense  in  which  the  major 
premise  of  a  valid  argument  is  the  proof  of  its 
conclusion. 

INDUCTION  FOUNDED  ON  INTUITION. 

The  question  now  is,  Where  did  we  get  that 
fundamental  principle?  It  is  absurd  to  con- 
sider it  an  induction,  as  we  have  seen,  on  Mr. 
Mill's  own  principles ;  it  must  then  be  a  deduc- 
tion or  an  intuition.  It  cannot  be  a  deduction, 
for,  as  Mr.  Mill  has  clearly  seen,  that  would 
suppose  a  principle  beyond  it  more  general 
from  which  it  was  derived.  Il  is  an  intuition, 
and  is  given  by  the  reason  in  its  primitive  un- 
foldings,  and  on  the  very  first  occasion  of  ihe 
recurrence  of  any  cause  whose  effect  we  have 
experienced,  or  of  any  cause  similar  to  that 
primary  cause.  We  see  its  manifestations  in 
the  very  first  rational  actions  of  the  child.     Let 


THE  PHILOSOPHY  OF  INDUCTION.         185 

bhe  child  put  his  finger  upon  a  coal  of  fire,  and 
he  learns  by  experience  that  it  causes  pain. 
Can  you  get  him  voluntarily  to  touch  it  a  second 
time  ?  He  sees  another  similar  coal  beside  it ; 
can  you  get  him  to  touch  that?  He  will  no 
sooner  touch  the  second  than  the  first.  Why 
not,  seeing  that  he  has  no  experience  but  that 
the  first  coal  was  once  the  cause  of  pain  ?  He 
knows  by  experience  nothing  about  its  powei 
to  burn  a  second  time,  and  nothing  at  all  about 
the  power  of  the  second  coal  to  burn.  The 
only  explanation  is,  that  his  reason  obliges  him 
to  conclude  as  he  does;  and  this  law  of  the 
reason,  this  principle  of  mental  order,  when 
rendered  into  language,  is  the  belief  that  like 
causes  produce  like  eflPects.  It  is  the  province 
of  the  philosopher  to  look  at  this  necessary 
movement  of  the  reason  and  to  abstract  from 
it  the  axiom  involved  in  it,  and  to  lay  it  as  the 
basis  of  all  formal  disquisitions  upon  the  laws 
of  nature.  But  the  child  is  guided,  nay,  he  is 
governed  by  it  in  all  his  future  inductions.  It 
transpires  in  the  reason  immediately  after  that 
great  first  principle  of  causality,  that  every 
event  has  a  cause,  which  is  as  early  as  our  first 
consciousness  of  sensation,  and  which  is  the  oc- 


136  ELEMENTS  OF  LOGIC. 

casion  of  our  primitive  ideas  of  the  external 
world,  and  of  God,  the  cause  of  causes,  and  laya 
the  foundation  of  all  science. 

Nor  is  the  principle  of  uniform  causation  in 
the  human  reason  alone ;  it  belongs  as  much  to 
the  instinct  of  animals  of  every  grade — the  fish, 
the  bird,  the  insect,  seems  infallibly  guided  by 
it.  It  pervades  the  whole  animated  world,  which 
without  it,  would  rush  on  instant  destruction. 
Indeed,  the  instinct  of  animals  goes  beyond  this, 
and  reveals  the  causative  character  of  many 
objects  before  any  experience  can  take  place  of 
their  power  to  bless  or  to  harm.  It  is  not  so 
with  man ;  he  must  test  everything  himself,  or 
be  taught  by  those  who  have  tested.  A  babe 
will  as  soon  put  his  hand  into  a  flame  as  snatch 
at  a  bouquet  of  flowers;  he  will  chew  the 
deadly  herb  as  fearlessly  as  the  lamb  would 
pluck  the  tender  grass. 

HUME'S  OPINION. 

This  fact  has  been  noticed  by  Mr.  Hume  with 
an  eagerness  which  characterizes  his  devotion 
to  empiricism.  He  then  takes  occasion  to 
wonder,  with  an  air  of  delighted  skepticism, 
how  it  is,  after   learning   thus   the   particular 


THE  PHILOSOPHY   OF  INDUCTION.         187 

character  of  causes,  we  can  infer  they  will  con- 
tinue to  produce  the  same  effects. 

"All  our  reasoning  on  matters  of  fact  seems 
to  be  founded  on  cause  and  effect.  By  means  of 
this  relation  alone  we  can  go  beyond  the  evi- 
dence of  our  memory  arid  senses.  If  you  were 
to  ask  a  man  why  he  believes  any  matter  of 
fact  which  is  absent ;  for  instance,  that  his 
friend  is  in  the  country  or  in  France,  he  would 
give  you  a  reason,  and  this  reason  would  be 
some  other  fact,  as  a  letter  received  from  him, 
or  a  knowledge  of  his  former  resolution.  A 
man  finding  a  watch,  or  any  other  machine, 
on  a  desert  island,  would  conclude  that  there 
had  once  been  men  in  that  island.  All  our 
reasonings  concerning  facts  are  of  the  same 
nature.  ...  If  we  would  satisfy  ourselves, 
therefore,  concerning  the  nature  of  that  evi- 
dence which  assures  of  matters  of  fact,  we  must 
inquire  how  we  came  at  the  knowledge  of  cause 
and  effect.  I  shall  venture  to  affirm,  as  a  gen- 
eral proposition,  which  admits  of  no  exception, 
that  the  knowledge  of  this  is  not  m  anyinstmic^ 
attained  hy  reasonings  a  priori^  hut  arises  en- 
tirely from  experience^  when  we  find  any  par 
ticular  objects  are  conjoined  with  each  other. 


138  ELEMENTS  OF  LOGIC. 

Let  any  object  be  presented  to  a  man  of  evei 
80  strong  natural  reason  and  abilities,  if  that 
object  be  entirely  new  to  him,  he  will  not  be 
able  by  the  most  accurate  examination  of  its 
sensible  qualities  to  discover  any  of  its  causes 
or  effects.  Adam,  though  his  rational  faculties 
be  supposed  at  the  very  first  entirely  perfect, 
could  not  have  inferred  from  the  fluidity  and 
transparency  of  water  that  it  would  suffocate 
him,  or  from  the  light  and  warmth  of  fire  that 
it  would  consume  him." 

All  this  we  see  no  reason  to  dispute ;  but 
when  he  advances  to  the  conclusion  that  it  is 
by  repeated  or  customary  experiences  that  w^e 
discover  the  uniformity  of  causation,  we  find 
him  as  blind  to  the  real  working  of  the  human 
reason  as  he  would  be  blind  to  the  operation  of 
animal  instincts  if  he  should  affirm  that  all 
animals,  like  man,  discover  all  noxious  food  and 
other  hurtful  causes  by  experience.  But  let 
Mr.  Hume  speak  for  himself  upon  this  point: 
"As  to  past  experience,  it  can  be  allowed  to  give 
direct  arid  certain  information  of  those  precise 
objects  only  and  that  precise  period  of  time 
which  fell  under  its  experience ;  but  why  this 
experience  should  extend  to  future  times  and  to 


THE    PHILOSOPHY    OF  INDUCTION.         139 

:)tlier  objects,  which,  for  aught  we  know,  may 
be  only  in  appearance  similar;  this  is  the  main 
question  on  which  I  insist.  The  bread  which  1 
formerly  ate  nourished  me ;  that  is,  a  body  of 
iuch  sensible  qualities  has  induced  secret 
powers.  But  does  it  follow  that  other  bread 
must  also  nourish  me  at  another  time,  and  that 
like  sensible  qualities  must  always  be  attended 
with  like  secret  powers?  The  consequence 
seems  to  be  no  wise  necessary.  At  least  it 
must  be  acknowledged  that  there  is  here  a  con- 
sequence drawn  by  the  mind,  that  there  is  a 
certain  step  taken,  a  process  of  thought,  or  in- 
ference, which  wants  to  be  explained.  These 
two  propositions  are  far  from  being  the  same. 
I  have  found  that  such  an  object  has  always 
been  attended  with  such  an  effect,  and  I  foresee 
that  other  objects,  which  are  in  appearance 
similar,  will  be  attended  with  similar  effects.  1 
shall  allow,  if  you  please,  that  one  proposition 
may  justly  be  inferred  from  the  other.  I  know, 
in  fact,  that  it  always  is  inferred.  But  if  you 
insist  that  the  inference  is  made  by  a  chain 
of  reasoning,  I  desire  you  to  produce  that 
reasoning." 

Eureka !  good  Mr.  Hume,  we  have  found  out 


140  ELEMENTS  OF   LOGIC. 

that  reasoning,  that  connecting  principle  which 
you  despaired  of  finding.  It  lay  just  before 
your  eyes  when  you  penned  the  observation 
that  one  proposition  is  always  inferred  from  the 
other.  Do  you  not  see  that  you  here  struck 
upon  a  law  of  the  reason  by  which  it  is  neceS' 
sitated  to  operate  thus,  and  that  this  law  ex- 
pressed in  language  is  the  axiom,  Like  causes 
produce  like  effects?  or,  as  it  is  generally  stated, 
The  course  of  nature  is  uniform.  What  men 
always  think  and  must  think  is  a  primary  and 
essential  truth,  an  ultimate  principle  of  reason. 
But  Mr.  Hume  has  objected  to  this  origin  of 
the  principle.  "  Were  it  the  offspring  of  the 
reason,  an  intuition,  it  would  be  as  perfect  at 
first  and  from  one  instance,  as  after  ever  so  long 
a  course  of  experience.  But  the  case  is  far 
otherwise.  Nothing  is  so  like  as  eggs ;  yet  no 
one,  on  account  of  this  apparent  similarity,  ex- 
pects the  same  taste  and  relish  in  all  of  them. 
It  is  only  after  a  long  course  of  experiments  in 
any  kind  that  we  attain  a  firm  reliance  and 
security  with  regard  to  a  particular  event 
Now,  where  is  that  process  of  reasoning  whitjh 
from  one  instance  draws  a  conclusion  so  differ- 
ent from  that  which  it  infers  from  a  hundred 


THE   PHILOSOPHY  OF  INDUCTION.         141 

instances,  tliat  are  nowise  different  from  that 
single  one?  This  question  I  propose  as  much 
for  the  sake  of  instruction  as  with  an  intention 
of  raising  difficulties.  I  cannot  find,  I  cannot 
imagine  any  such  reasoning." 

It  would  be  easy  to  turn  off  this  question 
with  a  joke,  especially  as  the  example  of  the 
eggs  is  so  egregiously  puerile ;  but  it  is  due  to 
the  candor  of  Mr.  Hume  to  treat  it  seriously, 
nay,  to  admit  that  the  question  is  one  of  great 
importance,  and  leads  to  the  true  science  of  in- 
duction. It  is  not  true  that  bodies  having  the 
same  or  similar  qualities  produce  different  ef- 
fects ;  the  eggs  that  have  a  different  taste  are 
different  in  some  particulars,  and  this  is  usually 
sufficiently  manifest  in  eggs;  and  if  your  eyes 
fail  to  see  it,  a  microscope  will  abundantly  re- 
veal it.  Just  here  opens  to  our  view  the  ap- 
propriate sphere  of  induction,  as  far  as  it  may 
be  properly  distinguished  from  deduction ;  its 
office  is  to  analyze  phenomena,  to  mark  the 
different  qualities  of  objects,  and  to  ascertain 
their  precise  effects ;  but  when  you  have  cer- 
tainly determined  what  qualities  in  any  case 
produce  what  effects,  one  single  instance  of 
causation  is  sufficient  for  the  widest  generali- 


142  ELEMENTS  OF  LOGIC. 

zation.  Show  me  the  property  of  the  magnol 
wliich  attracts  iron,  and  I  hesitate  not  to  pre- 
dict that  whenever  and  wherever  that  quality 
appears,  in  like  circumstances,  it  will  be  followed 
by  the  same  effect.  But  if  I  have  not  been 
careful  in  my  observations  and  mistaken  some 
other  property  for  the  real  one,  then  most  cer- 
tainly I  shall  make  a  false  prediction,  and  the 
event  will  expose  the  error.  It  is  not  in  the 
reason,  which  assures  me  intuitively  that  like 
causes  produce  like  effect^,  but  in  my  observa- 
tion. 

MERIT    OF    MILL. 

Science  is  under  no  greater  obligation  to  any 
writer  of  the  present  age  than  to  Mr.  John 
Stuart  Mill,  for  the  profound  and  elaborate  ex- 
position of  the  grounds  and  process  of  induction 
which  he  has  given  to  the  world.  "'  There  is  no 
event,"  he  remarks,  "  happening  in  the  uni- 
verse, which  is  not  connected  by  an  invariable 
sequence  with  some  one  or  more  of  the  phenom- 
ena which  preceded  it."  "  If  we  knew  all  the 
agents  which  exist  at  the  present  moment,  their 
collocation  in  space,  and  their  properties,  or  in 
other  words,  the  laws  or  modes  of  their  agency. 


THE   PHILOSOPHY  OF  INDUCTION.  148 

we  could  predict  the  whole  subsequent  histoij 
of  the  universe;  at  least,  unless  some  new  vo- 
lition of  a  power  capable  of  controlling  the 
anivei*se  should  supervene.  And  if  any  par- 
ticular state  of  the  universe  should  ever  recur  a 
second  time,  (which,  however,  all  experience 
combines  to  assure  us  will  never  happen,)  all 
subsequent  states  would  return  too,  and  history 
would,  like  a  circulating  decimal  of  many 
figures,  periodically  repeat  itself. 

"Jam  redit  et  virgo,  redeunt  Saturnia  regna, 
Alter  erit  turn  Tiphys,  et  altera  qii89  vehat  Argo 
Delectos  heroas :  erunt  quoque  altera  bella, 
Atque  itcrura  ad  Troiam  magnus  mittetur  Achilles." 

Such  undoubtedly  is  the  order  of  the  universe, 
with  the  single  exception  of  the  free-will  of 
moral  agents.  But  Mr.  Mill  makes  no  such 
exception,  for  he  holds  that  human  volitions  are 
BO  far  controlled  by  motives  that  a  man's  actions 
as  inevitably  result  from  his  character  as  any 
elfect  follows  a  cause ;  and  if  we  thoroughly 
knew  his  character  we  could  certainly  predict 
how  he  would  act  in  any  supposable  case.  But 
this  we  repudiate,  for  this  reason,  among  many 
which  cannot  now  be  mentioned,  that  the  same 


144  ELEMENTS  OF  LOGIC. 

view  must  apply  to  the  divine  mind  ;  and  then 
it  would  follow  that  the  universe,  like  a  circu- 
lating decimal,  actually  has  been,  and  will  be 
produced  and  destroyed,  again  and  again,  for- 
ever. For  God  is  the  same  in  character ;  and 
if,  when  nothing  was  but  he,  his  power  pro- 
duced the  present  universe,  it  was  but  the  type 
of  a  past  and  a  coming  eternity.  Plato's  rem- 
iniscences are  resurrections ;  and  not  only  the 
ideas  that  now  are  have  been  before,  but  we 
ourselves,  the  world's  millions,  and  all  their 
various  histories,  have  been  before  as  now,  and 
will  be  as  they  now  are,  again  and  again,  for- 
evermore.  But,  aside  from  free  agents,  the 
idea  of  Mr.  Mill  is  as  true  as  it  is  sublime ;  and 
it  illuminates  and  explains  the  problem  of  in- 
duction. The  law  of  causation  binds  together 
the  universe,  and  the  only  difficulty  is  to  dis- 
cover that  chain  amid  the  shifting,  and  veering, 
and  multitudinous  phenomena  that  move  about 
it  and  upon  it ;  but  if  you  can  strike  that  chain 
at  one  point  it  will  vibrate  throughout  its  whole 
direction.  "  The  order  of  nature,  as  perceived 
at  iirst  glance,  presents  at  every  instant  a 
chaos,  followed  by  another  chaos.  We  must 
decompose  each   chaos   into  single  facts.     We 


THE   PHILOSOPHY  OF  INDUCTION.  145 

must  learn  to  see  in  the  chaotic  antecedent  a 
multitude  of  distinct  antecedents,  and  in  the 
chaotic  consequent  a  multitude  of  distinct  con- 
sequents." What  then  ?  We  have  to  determine 
which  particular  antecedent  is  followed  by 
which  consequent,  and  which  consequent  is 
produced  by  which  antecedent;  then,  by  the 
simplest  ratiocination,  whose  major  premise  is 
the  principle  of  causality,  furnished  by  the 
reason,  we  generalize  the  fact,  or,  in  other 
words,  infer  a  law  of  nature.  To  make  the 
requisite  analysis  we  need  to  observe  and  ex- 
periment ;  and  we  require  no  aid  but  the  simple 
rules  of  arithmetic,  except  in  those  cases  where 
the  effects  of  various  causes  are  mixed  together, 
as  the  curvilinear  motion  of  the  rocket,  which 
is  the  result  of  various  causes.  Here  we  re- 
quire the  aid  of  the  higher  mathematics  tu  de- 
termine the  proportion  in  which  the  causes 
mingle  in  producing  the  effect.  But  all  mathe- 
matics is  deductive.  Hence,  nowhere  in  induc- 
tion, throughout  its  whole  circuit,  can  you  find 
any  new  principle  of  inference.  Inference, 
therefore,  is  always  one  and  the  same ;  it  is  a 
passage  of  tba  thought  from  the  more  general 

to  the  less  general,  or  to  the  particular;  and 
10 


146  ELEMENTS  OF   LOGIC. 

never  vice  versa,  from  the  particular  or  from 
particulars,  however  numerous,  to  the  general, 
I  repeat,  you  may  sum  them  up,  and  call  them 
bj  a  general  name ;  but  that  is  no  inference, 
no  induction,  nothing  but  generalization. 

CONCLUSION  OF  THE  ARGUMENT. 

Thus,  it  is  demonstrated  that  the  process  by 
which  we  discover  the  laws  of  nature  is  funda- 
mentally a  deductive  process ;  and  that  we  are 
as  much  indebted  to  the  reason  for  the  major 
premise  as  we  are  indebted  to  experience  for 
the  minor  premise. 

ARISTOTLE   VINDICATED. 

It  is  owing  to  a  misapprehension  of  the  in- 
tuitive developments  of  the  reason  that  some 
modern  philosophers  have  rejected  the  syllo- 
gism as  a  type  of  ratiocination.  They  suppose 
its  major  premise  is  a  general  truth  obtained  by 
a  summation  of  particulars ;  and,  consequently, 
to  deduce  one  of  these  particulars  from  the 
general  is  to  reason  in  a  circle.  But,  great  as 
the  mystery  of  the  reason  may  appear,  we  hold 
it  to  be  the  source  of  general  principles,  and  it 
gises  them  to  us  as  by  revelation.    So  struck 


THE   PHILOSOPHY   OF  INDUCTION.         147 

was  Cousin  with  this  function  of  reason  that  he 
seemed  well-nigh  beside  himself,  and  almost 
ready  to  bow  down  and  worship  it  as  a  portion 
of  divinity ;  and  Plato,  at  the  dawn  of  philoso- 
phy, declared,  "It  is  the  gift  of  the  gods  to 
man  which,  as  I  conceive,  they  sent  down  by 
some  Prometheus  in  a  blaze  of  light."  But  it 
is  no  enthusiasm  to  say  that  the  reason  is  the 
brightest  aspect  of  the  image  of  God  in  man. 
Were  the  human  mind  destitute  of  this  power 
of  intuition  it  would  be  impossible  to  vindicate 
the  logic  of  Aristotle.  This  he  clearly  saw  and 
stated  in  his  exposition  of  the  process  of  deduc- 
tion. Indemonstrable  truths,  he  aflSrms,  make 
the  basis  of  all  reasoning ;  for  if  your  premises 
be  demonstrated,  then  they  must  have  been  de- 
monstrated by  something  beyond  them,  and  if 
they  were  demonstrable  though  not  demon- 
strated, it  only  extends  the  chain  indefinitely 
back.  Hence  there  must  be  indemonstrable 
truths  at  the  foundation  of  every  reasoning  pro- 
cess, or  it  is  without  foundation.  And  these 
indemonstrable  truths  are  particular  intuitions 
of  sense,  of  consciousness,  and  of  the  reason,  and 
also  the  general  intuitions  or  principles  of  the 
reason.     Thus  sense  gives  us  direct  knowledge 


148  ELEMENTS  OF  LOGIC. 

of  the  qualities  of  bodies ;  consciousness,  of  the 
phenomena  of  mind;  and  reason,  ideas  of  sub* 
stance,  space,  time,  cause,  right  and  wrong,  and 
the  principles  of  causality,  mathematical  prin- 
ciples, etc.  The  principle  of  contradiction, 
namely,  a  thing  cannot  be  and  not  be  at  the 
same  time,  Aristotle  considered  the  first  of  these 
indemonstrable  principles,  which  lay  at  the 
foundation  of  demonstration. 

ERROR  OF    THE    SCHOOLMEN". 

The  error  of  the  schoolmen,  which  plunged 
them  into  the  vortex  of  abstract  speculation, 
and  for  which  Plato  is  to  be  blamed  rather  than 
Aristotle,  was  in  the  supposition  that  all  truth 
lay  wrapped  up  in  a  priori  principles,  and 
could  be  educed  by  ratiocination :  they  failed 
to  perceive  that  they  yielded  no  consequences 
of  scientific  value,  but  as  they  were  attached  to 
facts.  Bacon  reclaimed  science  from  folly  by 
turning  her  eye  upon  the  actual  phenomena  of 
nature.  But  it  is  an  illusion  as  great  as  that  of 
the  scholastics,  to  suppose  that  facts  can  of 
themselves  give  science;  for  they  are  as  incon- 
sequential without  the  principles  of  intuition  as 
these  are  barren  without  them ;  they  lie  scat- 


THE  PHILOSOPHY  OF  INDUCTIOK.  149 

tered  about  like  pebbles  on  tbe  shore,  antil  they 
are  bound  together  by  some  a  priori  principle 
or  general  truth ;  then  we  see  in  them  the  path 
of  the  mighty  laws  that  clasp  and  encircle  tho 
universe.  A  falling  apple  sheds  a  ray  of  light 
through  immensity,  and  a  drop  of  rain  marking 
the  clay  pours  its  illuminations  down  the  chasms 
of  a  past  eternity. 

And  is  not  here  the  answer  to  Mr.  Mill's  earn 
est  inquiry:  "  Why  is  a  single  instance  in  some 
cases  sufficient  for  a  complete  induction ;  while  in 
others,  myriads  of  concurring  instances,  without 
a  single  exception,  known  or  presumed,  go  so 
little  way  toward  establishing  a  universal  prop- 
osition ?"  The  difference  in  the  cases  is  that 
the  former  stands  in  the  relation  of  cause  and 
effect,  and  the  latter  does  not.  "  Whoever,"  he 
adds,  "  can  answer  this  question  knows  more 
than  the  wisest  of  the  ancients,  and  has  solved 
the  problem  of  induction."  Let  him  add  the 
true  theory  of  the  origin  of  primary  axioms  to 
his  own  incomparable  analysis  of  induction, 
and  he  may  demand  the  palm.  Take  away  the 
a  priori  principles  from  induction,  and  you 
cover  with  clouds  the  whole  process,  and  tbe 
long  »7ray  of  the  sciences  dependent  upon  it 


150  ELEMENTS  OF    LOGIC. 

restore  these  ideas  and  the  movement  is  attended 
with  certainty,  as  far  as  certainty  can  belong  to 
human  knowledge. 

I  say  as  far  as  certainty  belongs  to  human 
knowledge,  because,  after  all,  it  must  be  con- 
fessed that  absoluta  knowledge  is  not  for  man. 
In  its  very  depths  what  is  our  knowledge  bui 
faith  ?  When  we  talk  of  certainty  what  do  w€ 
mean  ?  Certainty  for  an  individual  is  but  his 
necessary  belief;  human  certainty  is  the  neces- 
sary and  universal  belief  of  the  race.  In 
heaven  itself  certainty  is  absolute  only  in  the 
Throne  of  Light ;  the  knowledge  of  the  loftiest 
archangel  nearest  that  Throne  is  but  a  cloudless 
belief,  forced  upon  his  understanding  by  its  own 
subjective  laws.  God  only  knows,  and  knows 
he  knows ;  God  only  is  light. 

SECOND   CAUSES. 

This  leads  us  to  remark,  that  the  problem  of 
induction  being  only  a  question  of  causation,  it 
matters  not  what  theory  any  one  adopts  in  re- 
spect to  second  causes,  if  he  admits  that  no 
event  is  without  a  cause,  and  like  causes  pro- 
duce like  effects,  that  is,  what  seems  to  us  to  be 
causes.     To  me,  however,  there  's  no  more  difl5« 


THE  PHILOSOPHY  OF  INDUCTION.  151 

culty  in  supposing  that  God  has  put  a  causative 
power  in  nature  distinct  from  his  own,  than 
that  he  has  constituted  nature,  both  matter  and 
mind,  distinct  from  his  own  essence.  If  matter 
exists  with  its  various  elements  distinct  from 
the  divine  nature,  though  not  independent  of 
it,  why  may  we  not  suppose  that  God  has  en- 
dued it  with  a  motive  property  as  well  as  other 
properties?  Secondary  causes  are  the  general 
belief  of  mankind  as  well  as  secondary  natures. 
Still,  you  may  take  either  hypothesis ;  you  may 
think  it  was  the  electric  fluid  which  struck  the 
oak  when  it  fell,  blasted  and  blazing  with  light- 
ning, or  you  may  regard  it  as  the  stroke  of  the 
divine  thought  or  volition,  and  think  that  all 
other  events  are,  in  like  manner,  the  extempo- 
raneous movements  of  the  all-pervading  mind 
of  Deity.  Yet  if  your  reason  obliges  you  to 
believe  that  they  proceed  upon  the  principles 
of  causality,  then  induction  is  the  same,  and  the 
certainty  of  its  results  is  the  same.  Proceeding 
upon  a  priori  and  empirical  data  conjointly, 
the  process  is  not  to  be  doubted  until  the  facul- 
ties of  observation  and  reason  are  doubted ;  and 
when  they  are  doubted  the  mind  is  ruined,  and 
the  light  of  knowledge  is  set  forever. 


II. 

MISCELLANEOUS  EXAMPLES   FOK 
PRACTICE. 

LESSON   I. 

1.  That  which  is  followed  by  repeptanoe  h 

not  to  be  desired  ; 
Some  pleasures  are  followed  by  repentanoe; 
Therefore,  some   pleasures  are  not   to   be 

desired. 

2.  If  the  world    existed   from   eternity  there 

would  be  records  prior  to  the  Mosaic; 

and  if  it  were   produced   by  chance  it 

would  not  bear  marks  of  design  ; 
But    there    are    no    records    prior    to    the 

Mosaic,   and   the   world    does   not   bear 

marks  of  design  ;  therefore, 
The  world  neither  existed  from  eternity,  noi 

is  it  the  work  of  chance. 

3.  Every  dispensation  of  Providence  is  bene- 

ficial ; 
Afflictions  are  dispensations  of  Providence : 
Therefore,  they  are  beneficial. 


EXAMPLES    FOR   PRACTICE.  153 

s 

4.  If  tl\ere   is*  a  God   he   ought  to  be_SEpr- 
^      shiped ;  ^- 

'^Bnt  there  is  a  Ggd  ;^ 

Therefore^  hf  ought  to  be  worshiped.  P 

5.  If  God  is  innnitely  wiseTand^acts  with  per- 

fect freedom,  he  does  nothing  but  what  ia 

best; 
But  God  is  infinitely  wise,  and  acts  with 

perfect  freedom ; 
Therefore,  he  does  nothing  but  what  is  best. 

6.  If  God  were  not  a  Being  of  infinite  good- 

ness, neither  would  he  consult  the  happi- 
ness of  his  creatures ; 

But  God  does  consult  the  happiness  of  his 
creatures ; 

Therefore,  he  is  a  Being  of  infinite  good- 


7j^  The  world  is  either  self-existent,  or  the  work 
of  soniefinite,  or  of  some  infinite  being ; 
But  it  is  not  self-existent,  nor  the  work  of  a 

finite„being ; 
Therefore,   it    is    the   work   of  an   infinite 
'    Being.  •      ^  j   ,  p 

8.  Ko  deceitful  msLf  merits  confidence ; 
All  honest  men"  merit  confid^ce  ; 
,  Therefore,  no  honest  man  is  deceitful. 


154  ELEMENTS  OF  LOGIC. 

9    Every  human  virtue  is  to  be  sought  with 
dih'gence ; 
Prudence  is  a  human  virtue; 
Therefore,  prudence  is  to  be  sought  iili- 
gently. 
10.  Everything  base  should  be  avoided  ; 
Some  pleasures  are  base ; 
Therefore,  some  pleasures  should  be  avoided. 

LESSOI^^  n. 

1.  He  who  follows  evil  counsel  will  meet  with 

trouble ; 
Rehoboam  followed  evil  counsel ; 
Therefore,  Rehoboam  met  with  trouble. 

2.  No  good  citizen  will  violate  the  laws  of  God 

and  man ; 
Duelists  do  that  which  violates  the  la\^a 

of  both  God  and  man ; 
Therefore,  duelists  are  not  good  citizens. 

3.  Things  offensive  to  delicacy  should  not  be 

used; 
Therefore,  some  words  should  not  be  used. 
4/  That  which  is  prudent  is  commendable ; 
Moderation  is  prudent; 
Therefore,  moderation  is  commendable. 


EXAMPLES  FOR    PRACTICE.  155 

5.  We   are   bound    to    set   apart  one  day  in 

seven  for  religious  duties,  if  the  fourth 
commandment  is  obligatory  on  us;  but 
we  are  bound  to  set  apart  one  day  in 
seven  for  religious  duties ;  and  hence  it 
appears  that  the  fourth  commandment  is 
obligatory  on  us. 

6.  A  desire  to  gain  by  another's  loss  is  a  viola- 

tion of  the  tenth  commandment ;  all 
gaming,  therefore,  since  it  implies  a  de- 
sire to  profit  at  the  expense  of  another, 
involves  a  breach  of  the  tenth  command- 
ment. 

7.  All  the  fish  that  the  net  inclosed  were  an 

indiscriminate  mixture  of  various  kinds : 
those  that  were  set  aside  and  saved  as 
valuable,  were  fish  that  the  net  inclosed; 
therefore,  those  that  were  set  aside  and 
saved  as  valuable  were  an  indiscriminate 
mixture  of  various  kmds. 

8.  No  one  who  lives  with  another  on  terms  of 

confidence  is  justified  on  any  pretense  in 
killing  him ;  Brutus  lived  on  terms  of 
confidence  with  Cesar;  therefore,  he  was 
not  justified,  on  the  pretense  he  pleaded 
in.  killing  him. 


156  ELEMENTS    OF   LOGIC. 

9.  Seeing  that  I  have  experienced  calamity  in 
the  snares  of  pleasure,  1  should  abandon 
its  pursuit. 
10.  The  principles  of  justice  are  variable;  the 
appointments  of  nature  are  invariable ; 
therefore,  the  principles  of  justice  are  no 
appointment  of  nature. 

LESSON  in. 

1.  All  good  Christians  are  saved ; 
All  good  Christians  have  sinned ; 
Therefore,  some  who  have  sinned  will  be 

saved. 

2.  Knowledge  is  better  than  riches ; 
Virtue  is  better  than  knowledge ; 
Therefore,  virtue  is  better  than  riches. 

3.  Christianity  requires  us  to  believe  what  the 

apostles  wrote ; 

St.  Paul  is  an  apostle ; 

Therefore,  Christianity  requires  us  to  believe 
what  St.  Paul  wrote. 
t.  It  is  necessary  that  a  general  should  under- 
stand the  art  of  war ; 

But  Caius  did  not  understand  the  art  of  war, 

Therefore,  it  is  necessary  that  Caius  should 
not  be  a  general. 


EXAMPLES   FOR   PRACTICE.  157 

5.  A  total  eclipse  of  the  sun  would  cause  dark- 
ness at  noon  : 
It  is  possible  that  the  moon  at  that  time  may 

totally  eclipse  the  sun  ; 
Therefore,  it  is  possible  that  the  moon  may 
cause  darkness  at  noon. 
6    The  fogs  vanish  as  the  sun  rises ; 

But  the  fogs  have  not  yet  begun  to  vanish 
Therefore,  the  sun  is  not  yet  risen. 

7.  The  sun  is  a  senseless  being ; 

What  the  Persians  worshiped  is  the  sun ; 
Therefore,  what  the  Persians  worshiped  is  a 
senseless  being. 

8.  If  every  creature  be  reasonable  every  brute 

is  reasonable ; 
But  no  brute  is  reasonable ; 
Therefore,  no  creature  is  reasonable. 

LESSON  rv. 
1 .  God  is  omnipotent ; 

An   omnipotent  being   can   do   everything 

possible  ; 
He  that  can  do  everytliing  possible  can  do 

whatever  involves  not  a  contradiction ; 
Therefore,  God  can  do  whatever  involves 
not  a  contradiction. 


168  ELEMENTS  OF   LOGIC. 

2.  If  we  love  any  person,  all  emotions  of  hatred 

toward  him  cease ; 

If  all  emotions  of  hatred  toward  a  person 
cease,  we  cannot  rejoice  in  his  mis- 
fortunes ; 

If  we  rejoice  not  in  his  misfortunes,  we  cer- 
tainly wish  him  no  injury ; 

Therefore,  if  we  love  a  person  we  wish  him 
no  injury. 

3.  A  thinking  substance  is  a  spirit; 
A  spirit  has  no  extension  ; 

What  has  no  extension  has  no  parts ; 

What  has  no  parts  is  indissohible ; 

Therefore,  the  mind  is  immortal. 
4r.  If  God  did  not  create  the  world  perfect  in 
its  kind,  it  must  either  proceed  from  w^ant 
of  inclination  or  from  want  of  power ; 

But  it  could  not  proceed  from  want  of  in- 
clination or  from  want  of  power ; 

Therefore,  God  created  the  world  pertect  in 
its  kind,  or,  which  is  the  same  thing,  it  is 
absurd  to  say  that  he  did  not  create  the 
world  perfect  in  its  kind. 
5.  Whatever  is  immaterial  is  indissoluble ; 

The  mind  of  man  is  immaterial ; 

Therefore,  the  mind  of  man  is  indissoluble 


EXAMPLES  FOR   PRACTICE.  169 

6.  Whatever  perceives,  judges,  and  reasons,  is 

a  thinking  substance; 
The  human   mind   perceives,  judges,  and 

reasons ] 
Therefore,  the  human  mind  is  a  thinking 

substance. 

7.  Things  equal  to  the  same  thing  are  equal  to 

one  another ; 
Therefore,  these  two  triangles,  each  equal 
to  the  square  of  a  line  of  three  inches, 
are  equal  between  themselves. 

8.  What  is  not  a  being,  since  it  can  have  no 

attributes,  can  be  no  agent  nor  act,  cannot 
produce  anything ; 
What  is  called  nothing  is  not  a  being,  has 
no  attribute,  is  not  an  agent,  nor  can  it 
act;  therefore,  what  is  called  nothing 
cannot  act  or  produce  anything. 

9.  The  order  and  constitution  of  things  estab- 

lished and  maintained  in  the  universe,  i? 

the  law  of  Supreme  intelligence ; 
Nature   is   the   order    and   constitution  ol 

things  established  and  maintained  in  the 

universe;  therefore. 
Nature  is  the  law  of  Supreme  intelligence 


160  ELEMENTS  OF   LOGIC. 

LESSON    V. 

1.  No  man  can  possess  power  to  pertonn  im 

possibilities ; 

A  miracle  is  an  impossibility  •; 

Therefore,  no  man  can  possess  power  to  per- 
form a  miracle. 

2.  War  is  the  source  of  numerous  evils ; 
Some  wars  are  just ;  therefore, 

Some  just  actions  are  the  source  of  numer- 
ous evils. 

3.  Protection  from  punishment  is  plainly  due 

to  the  innocent ;  therefore,  as  you  main- 
tain that  this  person  ought  not  to  be 
punished,  it  appears  that  you  are  con- 
vinced of  his  innocence. 

4.  All  the  most  bitter  persecutions  have  been 

religious  persecutions  ;  among  the  most 
bitter  persecutions  were  those  which  oc- 
curred in  France  during  the  Eevolutiou' 
therefore,  they  must  have  beer,  religious 
persecutions. 

5.  Of  two  evils  the  less  is  to  be  preferred ;  oc 

casional  turbulence,  therefore,  being  a 
less  evil  than  rigid  despotism,  is  to  be 
preferred  to  it. 


EXAMPLES  FOR  PRACTICE.  161 

6.  The  early  and   general  assignment  of  the 

Epistle  to  the  Hebrews  to  St.  Paul  as  its 
author,  must  have  been  either  from  its 
professing  to  be  his,  and  containing  his 
name,  or  from  its  really  being  his ;  since, 
therefore,  the  former  of  these  is  not  the 
fact,  the  epistle  must  be  Paul's.  • 

7 .  All  the  miracles  of  Jesus  would  fill  more  books 

than  the  world  could  contain  ;  the  things, 
related  by  the  evangelists  are  the  miracles 
of  Jesus;  therefore,  the  things  related  by 
the  evangelists  would  fill  more  books 
than  the  world  could  contain. 

8.  According    to    theologians,    a    man    must 

possess  faith  in  order  to  be  acceptable  to 
the  Deity ;  now  he  who  believes  all  the 
fables  of  the  Hindoo  mythology  must 
possess  faith ;  therefore,  such  a  one 
must,  according  to  theologians,  be  ac- 
ceptable to  the  Deity. 

9.  If  Abraham  were  justified,  it  must  have 

been  either  by  faith  or  by  works ;  now, 

he  was  not  justified  by  faith,  (according 

to  St.  James,)  nor  by  works,  (according 

to  St.  Paul ;)  therefore,  Abraham  was  not 

justified. 

11 


l$t  ELEMENTS  OF  LOGIC. 

to.  He  who  cannot  possibly  act  otherwise  than 
he  does  has  neither  merit  nor  demerit  in 
his  action  ;  a  liberal  and  benevolent  man 
cannot  possibly  act  otherwise  than  he 
does  in  relieving  the  poor ;  therefore, 
such  a  man  has  neither  merit  nor  demerit 
in  his  action. 


LESSON  VI. 

1.  Smollet,  in  a  town  in  France,  having  met  at 
an  inn  with  a  scolding  chambermaid  and  an 
awkward  red-haired  hostler,  who  had  engrossed 
his  whole  attention,  immediately  wrote  in  his 
journal:  "The  men  in  this  town  are  all  red- 
haired,  and  the  women  are  all  scolds." 

2.  The  Stoics  proved  that  the  world  was  a  great 
animal,  thus :  That  which  has  the  use  of  reason 
is  better  than  that  which  has  not.  Now,  there 
is  nothing  better  than  the  world ;  therefore,  the 
world  has  reason  and  is  a  great  animal. 

3.  The  Sophists  used  the  following  argument 
against  marriage :  If  a  woman  that  marries  be 
lovely  she  will  create  jealousies ;  if  she  be  ugly 
she  will  not  delight ;  therefore,  it  is  not  good  to 
marry. 


EXAMPLES  FOR   PRACTICE.  168 

4.  An  Irishman,  hearing  much  of  the  charms  of 
a  feather  bed,  took  a  feather  and  laid  it  on  a 
rock  for  a  pillow.  He  awoke  with  a  headache. 
'' Arrah,"  said  he,  "if  these  be  your  feathers  give 
me  my  straw." 

5.  Warm  countries  alone  produce  the  Banian- 
tree.  Spain  is  a  warm  country;  therefore, 
Spain  produces  the  Banian-tree. 

6.  A  canal  boat  was  passing  under  a  bridge, 
and  some  one  on  deck  cried  out,  "Look  out!" 
A  Dutchman  lying  in  his  berth  heard  the  cry, 
and  stuck  his  head  out  of  the  window,  and  re- 
ceived a  severe  blow  on  his  forehead.  "Vat 
for,"  cried  he,  in  a  passion,  "  did  you  tell  me  to 
'look  out?'  vy  did  you  not  tell  me  to  Mook 
in?'" 

7.  As  I  would  not  trifle  with  the  prejudices  of 
the  poor,  because  it  is  illiberal,  so  I  would  not 
always  yield  to  them,  because  it  is  unwise. 

8.  Books  are  seldom  correct,  because  human 
nature  is  fallible. 

9.  Fugitive  cant,  which  is  always  in  a  state  of 
increase  or  decay,  cannot  be  regarded  as  any 
part  of  the  durable  materials  of.  a  language,  and 
therefore  must  be  suffered  to  perish  with  other 
things  unworthy  of  preservation. 


164  ELEMENTS  OF  LOGIC 

10.  Pleasures  are  deceitful;   therefore,  young 
men  should  curb  their  Inclinations 


LESSON  vn. 

Let  the  learner  analyze  the  following,  giving, 
Ist,  the  terms;  2d,  the  propositions;  3d,  the 
syllogisms. 

Ye  men  of  Athens,  I  perceive  that  in  all 
things  ye  are  too  superstitious.  For  as  I  passed 
by  and  beheld  your  devotions  I  found  an  altar 
with  this  inscription  :  "  To  the  Unknown  God." 
Whom,  therefore,  ye  ignorantly  worship  him  de- 
clare I  unto  you.  God  that  made  the  world  and 
all  things  therein,  seeing  that  he  is  Lord  of 
heaven  and  earth,  dwelleth  not  in  temples  made 
with  hands;  neither  is  worshiped  with  men's 
hands,  as  though  he  needed  anything,  seeing 
he  giveth  to  all  life,  and  breath,  and  all  things ; 
and  hath  made  of  one  blood  all  nations  of  men 
for  to  dwell  on  all  the  face  of  the  earth,  and 
hath  determined  the  times  before  appointed, 
and  the  bounds  of  their  habitation ;  that  they 
should  seek  the  Lord,  if  haply  they  might  feel 
after  him  and  find  him,  though  he  be  not  fai 
from  every  one  of  us  :• 


EXAMPLES  FOE  PRACTICE.  166 

For  in  him  we  live,  and  move,  and  have  our 
being ;  as  certain,  also,  of  jour  own  poets  have 
said,  for  we  are  also  his  offspring. 

Forasmuch,  then,  as  we  are  the  offspring  of 
God,  we  ought  not  to  think  that  the  Godhead  is 
like  unto  gold,  or  silver,  or  stone,  graven  by  art 
and  man's  device. 

And  the  times  of  this  ignorance  God  winked 
at,  but  now  commandeth  all  men  everywhere  to 
repent ; 

Because  he  hath  appointed  a  day  in  the 
which  he  will  judge  the  world  in  righteousness 
by  that  man  whom  he  hath  ordained ;  whereof 
he  hath  given  assurance  unto  all  men  in  that  he 
hath  raised  him  from  the  dead. 

LESSON   VHL 

Arguments  from  uivpubUshed    documents. 

1*  If  the  Mosaic  doctrine  of  the  absolute  crea- 
tion of  the  world  out  of  nothing,  by  the 
divine  decree,  were  unreasonable,  ft 
would  have  shocked  the  common  mind. 

2.  If  Pantheism  be  true,  and  all  things  are  but  a 
development  of  the  Deity,  then  the  idea 
of  cause  in   the  human   mind  is  an  11- 


t66  ELEJfENTS  OF  LOGIC. 

liision,  for  in  that  case  it  is  nowhere  fully 
realized,  as  modifications  are  not  abso- 
lute causations. 

8.  Though  we  cannot,  with  Plato  and  Cousin, 
regard  the  reason  in  man  as  itself  divine, 
it  is  certainly  perfect ;  and  is,  therefore, 
as  a  perfect  creation,  evidence  of  a  per- 
fect Creator. 

4.  Kg  interpretation  of  the  Bible  is  to  be  con- 
sidered correct  which  is  directl}^  opposed 
to  the  absolute  principles  of  reason,  for 
this  would  be  suicidal,  inasmuch  as  every 
argument  for  the  divine  inspiration  of  the 
Bible  is  based  upon  those  very  prin- 
ciples. 

6.  If  the  New  Testament  be  ngt  a  true  history 
of  Christ,  it  is  the  greatest  romance  in  all 
literature;  and  if  it  be  the  greatest  ro- 
mance ever  written,  its  author  could  not 
have  been  unknown  to  his  cotempo- 
raries. 

6.  If  the  story  of  the  resurrection  be  true,  the 
Christian  religion  is  proved  to  be  of  di- 
vine origin  ;  if  it  be  false,  no  explanation 
can  bfe  given  of  the  sudden  and  extensive 
spread  of  the  Christian  faith. 


EXAMPLES  FOR  PRACTICE.  167 

7,  The  Bible  must  be  of  divine  origin,  for  its 
production  is  beyond  all  example  of  human 
genius 


The  remamder  are  from  notes  of  Dr,  Whedon. 

8.  Every  necessary,  universal,  and  perpetual 

idea  is  a  truth ; 
Immortality  is  such  an  idea ; 
Therefore,  immortality  is  a  truth. 

9.  Nothing  is  to  be  held  eternal  which  we  can 

rationally  conceive  once  to  have  not  ex- 
isted, and  the  infinite  space  to  be  vacant 
of  it. 

10.  Nothing  is  by  the  laws  of  the  mind  to  be 
held  as  having  no  beginning,  which  we 
can  rationally  conceive  to  have  once  non- 
existed  and  then  begun.  Now  of  the 
visible  material  world  we  can  conceive 
space  to  have  been  empty,  we  can  con- 
ceive that  it  once  nonexisted  and  then 
began.  Not  so  of  space  or  of  creative 
mind.  In  order  to  the  world's  beginning, 
these  must  have  preceded  and  never 
have  had  a  beginning. 


i68  ELEMENTS  OF    LOGIC. 

11.  The  regular  organrzation  of  the  world  must 

either  be  eternal,  or  formed  without  de- 
sign, or  formed  by  design ; 

The  regular  organization  of  the  world  can- 
not be  eternal ;  for  geology  shows  it  to  be 
composed  of  elements  once  inorganic. 

The  regular  organism  of  the  world  cannot 
be  without  design,  for  no  complex  adjust- 
ment of  parts  to  accomplish  an  end  can 
exist  without  design. 

12.  The  regular  organization  of  the  world  is  by 

design,  for  it  accords  with  all  the  laws  of 
design,  and  with  nothing  else  that  we 
know. 

LESSON   LX. 

Sv^osed  Exceptions  to  Rules. 

Hamilton,  Thompson,  and  our  own  country- 
man, Mahan,  and  others,  have  suggested  several 
alterations  in  the  forms  of  Logic,  as  left  by 
Aristotle ;  but  with  deference  to  these  original 
thinkers,  I  consider  them  unnecessary  and  in- 
expedient. To  try  the  skill  of  the  advanced 
student,  and  to  make  this  book  as  complete 
as  may  be,  without  an  adequate  discussion 
of  these  topics,  the  present  lesson  will  contain 


EXAMPLES  FOR  PHACTICE.  169 

specimens  of  those  propositions  and  arguments 
which  have  been  supposed  to  be  exceptions  to 
the  rules  and  to  require  a  re-formation  of  the 
science. 

Eight  Classes  of  Propositions^  i/nstead  of  the 
fouvy  A^  E^  /,  O^of  Aristotle, 

1.  Toto- total.  All  A  is  all  of  B. — All  men  are 

all  rational  animals. 

2.  Toto-partial.  All  A  is  some  of  B. — All  men 

are  mortal. 

3.  Parti-total.  Some  A  is  all  of  B. — Some  men 

are  all  the  sailors. 

4.  Parti-partial.  Some  A  is  some  of  B. — Some 

men  are  sailors. 
6.  Toto-total.  Any  A  is  not  any  B. — ^No  man  is 
a  brute. 

6.  Toto-partial.  Any  A  is  not  some  B. — l^o  man 

is  some  brute. 

7.  Parti-total.    Some  A  is  not  any  B. — Some 

men  are  no  brutes. 
8    Parti-partial.  Some  A  is  not  some  B. — Seme 
men  are  not  some  brutes. 
Thompson  makes  but  six. 

A.  All  plants  grow. 

E.  No  right  action  is  inexpedient. 


1 70  ELEMENTS  OP  LOGIC. 

I.  Sone  muscles  act  without  voiition. 
O.  Some  plants  do  not  grow  in  the  tropins 
(J.  Commoa  salt  is  chloride  of  sodium. 
Y.  Some  stai"*  are  all  planets. 

Hamilton  and  Mahan  add : 

0).  Some  X  is  not  some  Y. 
Tf.  No  X  is  some  Z. 

A  is  converted  into  Y. 


E 

U 

u 

E. 

I 

U 

u 

1. 

O 

u 

u 

V' 

U 

(( 

(( 

u. 

T 

u 

ti 

A. 

w 

a 

u 

a. 

<» 

u 

ii 

0. 

If  we  admit  Sir  William  Hamilton's  doctrine 
of  the  Quantification  of  the  Predicate^  namely, 
that  if  you  refer  not  to  the  form  of  expression, 
but  to  what  is  meant  by  it,  \hQ  jpredicate  has  air 
ways  a  definite  quantity^  and  the  propositM^i 
may  always  he  converted  simply  j  still  this  very 
difference  between  the  form  of  a  proposition 
and  its  meaning,  makes  it  necessary  to  have 
lules  to  determine  what  is  the  extent  of  the 


EXAMPLES  FOR  PKACTICE.  17  J 

predicate  and  to  govern  conversion ;  and  no 
rules  are  better  than  those  of  Aristotle,  if  we 
keep  in  mind  the  exceptions  to  the  rules  I  have 
made.     (See  Section  on  Distribution.) 

EXAMPLES    OF   IMMEDIATE   INFERENCE. 

These  supposed  inferences  will  be  found  to 
be  either  the  same  as  the  premise  in  different 
language,  or  derived  from  it  by  means  of 
another  premise  understood,  or  by  conversion. 

IMMEDIATE  INFERENCE  BY  MEANS  OP  PRIVA- 
TIVE  CONCEPTIONS. 

L  The  Premise^  a  PosiUve  GoncepUon. 

A.  All  the  righteous  are  happy ; 

Therefore,   none  of  the  righteous  are  un- 
happy; 
And,  all  who  are  unhappy  are  unrighteous. 
E,  No  human  virtues  are  perfect ; 

Therefore,  all  human  virtues  are  imperfect; 
And,  all  perfect  virtues  are  not  human. 
I.  Some  possible  cases  are  probable ; 

Therefore,  some  possible  cases  are  not  im 

probable ; 
And  some  probable  cases  are  not  impossible. 


172  ELEMENTS  OP    LOGIC. 

0.  Some  possible  cases  are  not  probable ; 
Therefore,    some    possible    cases    are    im 

probable ; 

And,  some  improbable  cases  are  not  im- 
possible. 
U.  The  just  are  [all]  the  holy ; 

Therefore,  all  unholy  men  are  unjust ; 

And,  no  just  men  are  unholy. 
r.  Some  happy  persons  are  [all]  the  righteous ; 

Therefore,  all   who    are    unhappy  are   un- 
righteous ; 

And,  no  righteous  persons  are  unhappy. 

IL  The  Premise^  a  Privative  Concejption, 
A.  All  the  insincere  are  dishonest ; 

Therefore,  no  insincere  man  is  honest ; 

And,  all  honest  men  are  sincere. 
E.  No  unjust  act  is  unpunished ; 

Therefore,  all  unjust  acts  are  punished ; 

And,  all  acts  not  punished  are  just. 

1.  Some  unfair  acts  are  unknown  ; 
Therefore,  some  unfair  acts  are  not  known ; 
And,  some  unknown  acts  are  not  fair. 

0.  Some  improbable  cases  are  not  impossible; 
Therefore,  some  improbable  cases  are  pos- 
sible ; 
A.nd,  some  possible  cases  are  not  probable 


EXAMPLES  FOR   PRACTICE.  173 

U.  The  unlawful  is  the  [only]  inexpedient ; 

Therefore,  the  lawful  is  the  expedient ; 

And  the  lawful  is  not  the  inexpedient. 
Y   Some  unhappy  men  are  [all]  the  unright- 
eous ; 

Therefore,  no  happy  men  are  unrighteous ; 

And,  some  unhappy  men  are  not  righteous. 


IMMEDIATE    INFEEENCE    BY    ADDED    DETERM* 
INANTS. 

A  servant  is  a  fellow-creature ; 

Therefore,  a  servant  in  suffering  is  a  fellow- 
creature  in  suffering. 

Virtue  deserves  respect,  and  a  servant  is  a 
fellow-creature ; 

Therefore,  a  virtuous  servant  is  a  fellow- 
creature  deserving  of  respect. 


IMMEDIATE  ESTFERENCE  BY  CO^IPLEX  CONCEP 
TION. 

Oxygen  is  an  element,  so  that  the  decompo- 
sition of  oxygen  would  be  the  decomposition  of 
an  element. 


L74  ELEMENTS  OF   LOGIC. 

IMMEDIATE  Il^TERENOES  OF  INTERPRETATION. 

All  the  Gentiles  are  also  called ;  that  is,  all 
other  nations,  as  well  as  the  Jewish,  are  called. 

Howard  exhibited  this  high  philanthropic 
spirit ; 

Therefore,  snch  philanthropy  really  exists. 

A  is  B ;  therefore,  B  exists. 

A  is  B ;  therefore,  where  A  is  we  find  B. 


niMEDIATE  INFERENCE  FROM  A   DISJUNCTIVE 
JUDGMENT. 

All  teeth  are  either  incisors,  canine,  bicuspid, 
or  molar ; 

Therefore,  the  molar  teeth  are  neither  incisors, 
canine,  nor  bicuspid ; 

And,  all  teeth  which  are  not  molar  are  either 
canine,  incisors,  or  bicuspid. 


IMMEDIATE   INFERENCE   BY   THE   SUM   OF 
SEVERAL   PREDICATES. 

Copper  is  a  metal  of  a  red  color  and  dis- 
agreeable smell  and  taste,  all  the  properties  of 
which  are  poisonous ;  which  is  highly  malleable, 


EXAMPLES  FOR  PRACTTCE.  176 

ductile,   tenacious,  with    a   specific  gravity  of 
about  8.83 ; 

Therefore,  a   metal  of  a  red  color,  etc.,  is 
copper. 


UNFIGURED   SYLLOGISM. 

In  the  unfigured  syllogism  of  Hamilton  and 
Mahan  the  terms  compared  do  not  stand  to  each 
other  in  the  relation  of  subject  and  predicate, 
being  in  the  same  proposition  either  hoth  sub- 
jects  or  hoth  jpredicates. 

All  C  and  some  B  are  equal ; 

All  A  and  all  B  are  equal ;  , 

Therefore,  all  C  and  some  A  are  equal ; 

Or,  C  and  A  are  unequal. 

Copperas  and  sulphate  of  iron  are  identical ; 

Sulphate  of  iron  and  sulphate  of  copper  are 
not  identical ; 

Therefore,  copperas  and  sulphate  of  copper 
are  not  identical. 

Alio  and  all  B  equal  Y; 
All  A  and  all  B  do  not  equal  Y ; 
Therefore,  0  and  A  are  not  equal  to  each 
other 


176  ELEMENTS  OF  LOGIC. 

C  and  B  always  coexist,  or  are  universally 
compatible ; 

A  and  B  never  coexist,  or  are  wholly  incom- 
])atible ; 

Therefore,  C  and  A  never  coexist,  or  are  not 
compatible. 

Some  of  these  unfigured  syllogisms,  upon  anal- 
ysis, will  be  found  to  contain  one  or  two  other 
syllogisms  with  premises  suppressed.  In  the  first 
instance  given,  ''''Things  equal  to  the  sa/me  thing 
are  equal  to  each  other^'^  is  the  implied  premise. 

REASONING  FROM  WHOLES  IN  COMPREHENSION. 

Sir  William  Hamilton's  discovery  is  illusory ; 
an  individual  cannot  comprehend  a  species,  nor 
a  species  a  genus.  This  red  rose  is  both  in  ex- 
tension and  comprehension  one,  A  single  rose 
with  its  own  red;  it  cannot  comprehend  red 
rose^  which  is  not  ordy  this^  hut  that^  and  all 
other  red  roses  /  and  it  admits  of  no  inference. 
A  thing  is  itself  and  not  something  else  how- 
ever like  it,  much  less  its  class.  So  triangle 
comprehends  not  figure^  but  only  the  thre& 
cmgled  portion, 

THE  END. 


VB 


95 


